CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 2 - MCQExams.com

The equation of the image of the circle $$x^{2}+y^{2}-6x-4y+12=0$$ by the line mirror $$x+y-1=0$$ is
  • $$x^{2}+y^{2}+2x+4y+4=0$$
  • $$x^{2}+y^{2}-2x+4y+4=0$$
  • $$x^{2}+y^{2}+2x+4y-4=0$$
  • $$x^{2}+y^{2}+2x-4y+4=0$$
The locus of a point which moves such that the sum of the squares of its distances from three vertices of a triangle ABC is constant is a circle
whose centre is at the
  • centroid of triangle ABC
  • Circumcentre of triangle ABC
  • Orthocentre of triangle ABC
  • incentre of triangle ABC
The lines 2x-3y $$=5$$ and 3x-4y $$=7$$ diameters of a circle having area as $$154$$ units. Then the equation of the circle is:
  • $$x^{2}+y^{2}-2x+2y=62$$
  • $$x^{2}+y^{2}+2x+2y=62$$
  • $$x^{2}+y^{2}+2x-2y=47$$
  • $$x^{2}+y^{2}-2x+2y=47$$
lf the line $$3{x}-2{y}+6=0$$ meets $${x}$$-axis, $$y$$-axis respectively at $${A}$$ and $${B}$$, then the equation of the circle with radius $${A}{B}$$ and Centre at $${A}$$ is
  • $$x^{2}+y^{2}+4x+9=0$$
  • $$x^{2}+y^{2}+4x-9=0$$
  • $$x^{2}+y^{2}+4x+4=0$$
  • $$x^{2}+y^{2}+4x-4=0$$
lf the lines $$2x+3y+1=0$$ and $$3x-y-4=0$$ lie along diameters of a circle of circumference $$ 10\pi$$, then the equation of the circle is:
  • $$x^{2}+y^{2}-2x+2y-23=0$$
  • $$x^{2}+y^{2}-2x-2y-23=0$$
  • $$x^{2}+y^{2}+2x+2y-23=0$$
  • $$x^{2}+y^{2}+2x-2y-23=0$$
lf the lines $$2x-3y=5$$ and $$3x-4y=7$$ are two diameters of a circle of radius $$7$$ then the equation of the circle is
  • $$x^{2}+y^{2}+2x-4y-47=0$$
  • $$x^{2}+y^{2}=49$$
  • $$x^{2}+y^{2}-2x+2y-47=0$$
  • $$x^{2}+y^{2}=17$$
A line is at a constant distance $$c$$ from the origin and meets the coordinates axes in $$A$$ and $$B$$. The locus of the centre of the circle passing through $$O, A, B$$ is
  • $$x^{-2} + y^{-2} = c^{-2}$$
  • $$x^{-2} + y^{-2} = 2c^{-2}$$
  • $$x^{-2} + y^{-2} = 3c^{-2}$$
  • $$x^{-2} + y^{-2} = 4c^{-2}$$
The area of a circle centered at $$(1,2)$$ and passing through $$(4,6)$$ is
  • $$5\pi$$ sq. units
  • $$15\pi$$ sq. units
  • $$25\pi$$ sq. units
  • $$30\pi$$ sq. units
The equation of the circle passing through the point $$(-1,2)$$ and having two diameters along the pair of lines $$\mathrm{x}^{2}-\mathrm{y}^{2}-4\mathrm{x}+2\mathrm{y}+3=0$$ is
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}-4\mathrm{x}-2\mathrm{y}+5=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+4\mathrm{x}+2\mathrm{y}-5=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}-4\mathrm{x}-2\mathrm{y}-5=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+4\mathrm{x}+2\mathrm{y}+5=0$$
The eccentricity of the conic represented by $$\sqrt{(x+2)^{2}+y^{2}}+\sqrt{(x-2)^{2}+y^{2}}=8$$ is 
  • $$\displaystyle \frac{1}{3}$$
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{1}{4}$$
  • $$\displaystyle \frac{1}{5}$$
The total number of real tangents that can be drawn to the ellipse $$3x^{2}+5y^{2}=32$$ and $$25x^{2}+9y^{2}=450$$ passing through $$(3,5)$$ is
  • $$0$$
  • $$2$$
  • $$3$$
  • $$4$$
The centre, vertex, focus of a conic are $$(0,0),
(0,5), (0,6)$$. Its length of latus rectum is
  • $$\dfrac{11}5$$
  • $$\dfrac75$$
  • $$\dfrac{14}5$$
  • $$\dfrac{22}5$$
The length of the latus rectum of the hyperbola $$x^{2}-4y^{2}=4$$ is
  • $$2$$
  • $$1$$
  • $$4$$
  • $$3$$
A straight line is drawn through the centre of the circle $${x}^{2}+{y}^{2}=2ax$$ parallel to $${x}+2y=0$$ and intersecting the circle at $${A}$$ and $${B}$$. Then, the area of $$\Delta A{O}{B}$$ is
  • $$\displaystyle \dfrac{\mathrm{a}^{2}}{\sqrt{5}}$$
  • $$\displaystyle \dfrac{\mathrm{a}^{3}}{\sqrt{5}}$$
  • $$\displaystyle \dfrac{\mathrm{a}^{2}}{\sqrt{34}}$$
  • $$\displaystyle \dfrac{\mathrm{a}^{2}}{\sqrt{3}}$$
The length of latus rectum of the hyperbola $$4x^{2}-9y^{2}-16x-54y-101=0$$ is
  • $$\dfrac85$$
  • $$\dfrac87$$
  • $$\dfrac89$$
  • $$\dfrac83$$
The equation  $$\sqrt{(x-2)^{2}+y^{2}}+\sqrt{(x+2)^{2}+y^{2}}=5$$ represents
  • a circle
  • ellipse
  • line segment
  • an empty set
The equation of directrix and latus rectum of a parabola are $$3x-4y+27=0$$ and $$3x-4y+2=0$$. Then the length of latus rectum is
  • $$5$$
  • $$10$$
  • $$15$$
  • $$20$$
A circle of radius $$5$$ units passes through the points $$(7,1),(9,5)$$. If the ordinate of the centre is less than $$2$$, then the equation of the circle is
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+8\mathrm{x}-10\mathrm{y}+16=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+8\mathrm{x}+10\mathrm{y}+16=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}-24\mathrm{x}-2\mathrm{y}+120=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+24\mathrm{x}-2\mathrm{y}-120=0$$
The equation $$(\mathrm{x}^{2}-\mathrm{a}^{2})^{2}+(\mathrm{y}^{2}-\mathrm{b}^{2})^{2}=0$$ represent points which are
  • collinear
  • on a circle centre $$(a,b)$$
  • on a circle centre $$(0,0)$$
  • coincident
Assertion(A): The difference of the focal distances of any point on the hyperbola $$\displaystyle \frac{x^{2}}{36}-\frac{y^{2}}{9}=1$$ is 12.
Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis
  • Both A and R are true and R is the correct

    explanation of A.
  • Both A and R are true but R is not the correct

    explanation of A.
  • A is true but R is false.
  • A is false but R is true.
A parabola with axis parallel to $$x$$ axis passes through $$(0, 0), (2, 1), (4, -1).$$ Its length of latus rectum is
  • $$\displaystyle \frac{2}{3}$$
  • $$\displaystyle \frac{1}{4}$$
  • $$\displaystyle \frac{7}{3}$$
  • $$\displaystyle \frac{1}{3}$$
Length of the latusrectum of the hyperbola $$xy=c$$ ,is equal to
  • $$2c$$
  • $$\sqrt{2}c$$
  • $$2\sqrt{2}c$$
  • $$4c$$
The difference between the length $$2a$$ of the transverse axis of a hyperbola of eccentricity $$e$$ and the length of its latus rectum is :
  • $$2a\left| 3-{ e }^{ 2 } \right| $$
  • $$2a\left| 2-{ e }^{ 2 } \right| $$
  • $$2a\left( { e }^{ 2 }-1 \right) $$
  • $$a\left( 2{ e }^{ 2 }-1 \right) $$
The length of the latus rectum of the parabola, whose focus is $$\left(\displaystyle \frac{u^{2}}{2g}\sin 2\alpha,\frac{-u^{2}}{2g}\cos 2\alpha \right)$$ and directrix is $$y=\dfrac{u^{2}}{2g}$$, is
  • $$\displaystyle \frac{u^{2}}{g}\cos^{2}\alpha$$
  • $$\displaystyle \frac{u^{2}}{g}\cos 2\alpha$$
  • $$\displaystyle \frac{2u^{2}}{g}\cos 2\alpha$$
  • $$\displaystyle \frac{2u^{2}}{g}\cos^{2}\alpha$$
A parabola has x- axis as its axis, y- axis as its directrix and $$4a$$ as its latus rectum. If the focus lies to the left side of the directrix then the equation of the parabola is
  • $$y^{2}=4a(x+a)$$
  • $$y^{2}=4a(x-a)$$
  • $$y^{2}=-4a(x+a)$$
  • $$y^{2}=4a(x-2a)$$
If $$L_{1}L_{2}$$ is the latusrectum of $$y^{2}=12x$$,  $$P$$ is any point on the directrix then the area of $$\Delta PL_{1}L_{2}$$ =
  • $$32$$
  • $$18$$
  • $$36$$
  • $$16$$
The length of latus rectum of the parabola $$(x-2a)^{2}+y^{2}=x^{2}$$ is
  • $$2a$$
  • $$3a$$
  • $$6a$$
  • $$4a$$
The length of latus rectum of the parabola $$y^{2}+8x-2y+17=0$$ is
  • $$2$$
  • $$4$$
  • $$8$$
  • $$16$$
The length of latus rectum of the hyperbola $$xy-3x-3y+7=0$$ is
  • $$4$$
  • $$3$$
  • $$2$$
  • $$1$$
The equation of the circle having centre $$(1,\ -2)$$ and passing through the point of intersection of the lines $$3x+y=14$$ and $$2x+5y=18$$ is
  • $$x^2+y^2-2x+4y-20=0$$
  • $$x^2+y^2-2x-4y-20=0$$
  • $$x^2+y^2+2x-4y-20=0$$
  • $$x^2+y^2+2x+4y-20=0$$
The centre of a circle is $$(2a, a-7$$). Find the values of $$a$$ if the circle passes through the point (11, -9) and has diameter $$10\sqrt{2}$$ units.
  • $$\dfrac 35$$
  • $$ 3 $$
  • $$ 5 $$
  • $$\dfrac 53$$
The equation of parabola whose latus rectum is $$2$$ units, axis is $$x+y-2=0$$ and tangent at the vertex is $$x-y+4=0$$ is given by
  • $$(x+y-2)^{2} = 4\sqrt{2}(x-y+4)^{2}$$
  • $$(x-y-4)^{2} = 4\sqrt{2}(x+y-2)$$
  • $$(x+y-2)^{2} = 2\sqrt{2}(x-y+4)$$
  • $$(x-y-4)^{2} =2\sqrt{2}(x-y+2)^{2}$$
$$(4-\mathrm{a})\mathrm{x}^{2}+(12-\mathrm{a})\mathrm{y}^{2}=\mathrm{a}^{2}-16\mathrm{a}+48$$ represents an ellipse. Then:
  • $$a<12$$
  • $$a<4$$
  • $$a>4$$ & $$a<12$$
  • $$a>0$$
Latus rectum of a parabola is a ........ line segment with respect to the axis of the parabola through the focus whose endpoints lie on the parabola.
  • perpendicular
  • parallel
  • tilted
  • None of these
Which of the following is/are not false?
  • The mid point of the line segment joining the foci is called the centre of the ellipse.
  • The line segment through the foci of the ellipse is called the major axis.
  • The end points of the major axis are called the vertices of the ellipse.
  • Ellipse is symmetric with respect to Y-axis only.
The arrangement of the following parabolas in the ascending order of their length of latusrectum 
A)   $$y=4x^{2}+x+1$$     B) $$2y=x^{2}+x+5$$
C)   $$x=2y^{2}+y+3$$     D) $$y^{2}+x+y+9=0$$
  • $$B,D,C,A$$
  • $$A,B,C,D$$
  • $$A,C,D,B.$$
  • $$A,D,C,B$$
If $${a}\neq 0$$ and the line  $$2{b}{x}+3 cy+4{d}=0$$ passes through the points of intersection of the parabolas $${y}^{2}=4ax$$ and $${x}^{2}=4ay,$$ then
  • $${d}^{2}+(2{b}+3{c})^{2}=0$$
  • $${d}^{2}+(3{b}+2{c})^{2}=0$$
  • $${d}^{2}+(2{b}-3{c})^{2}=0$$
  • $${d}^{2}+(3{b}-2{c})^{2}=0$$
If the equation of the incircle of an equilateral triangle is $${ x }^{ 2 }+{ y }^{ 2 }+4x-6y+4=0$$, then the equation of the circumcircle of the triangle is
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x+6y-23=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x-6y-23=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x-6y-23=0$$
  • None of these
The length of the latus rectum of the parabola 
$$169\left \{ (x-1)^{2}+(y-3)^{2} \right \}=(5x-12y+17)^{2}$$ is
  • $$\dfrac{14}{11}$$
  • $$\dfrac{12}{13}$$
  • $$\dfrac{28}{13}$$
  • none of these
The equation of a locus is $$y^{2}+2ax+2by+c=0$$. Then
  • it is an ellipse
  • it is a parabola
  • latus rectum $$=a$$
  • latus rectum $$=2a$$
$$\dfrac {x^2}{r^2-r-6}+\dfrac {y^2}{r^2-6r+5}=1$$ will represents the ellipse, if r lies in the interval:
  • $$(-\infty, -2)$$
  • $$(3, \infty)$$
  • $$(5, \infty)$$
  • $$(1, \infty)$$
The equation $$x^{2}+y^{2}-2x+4y+5=0$$ represents 
  • a point
  • a pair of straight lines
  • a circle of non zero radius
  • none of these
If major axis is the x-axis and passes through the points $$(4, 3)$$ and $$(6, 2)$$, then the equation for the ellipse whose centre is the origin is satisfies the given condition.
  • $$\displaystyle \frac{x^2}{52} + \frac{y^2}{13} =1$$
  • $$\displaystyle \frac{x^2}{13} + \frac{y^2}{52} =1$$
  • $$\displaystyle \frac{x^2}{52} - \frac{y^2}{13} =1$$
  • $$\displaystyle \frac{x^2}{13} - \frac{y^2}{52} =0$$
The equation $$7y^2-9x^2+54x-28y-116=0$$ represents
  • a hyperbola
  • a parabola
  • an ellipse
  • a pair of straight lines
If the parabola $$y^{2}=4ax$$ passes through $$(3,\:2)$$ then the length of latus rectum is
  • $$\displaystyle \frac{1}{3}$$
  • $$\displaystyle \frac{2}{3}$$
  • $$1$$
  • $$\displaystyle \frac{4}{3}$$
The equation of the circle passing through the point $$(1, 1)$$ and having two diameters along the pair of lines $$x^{2}-y^{2}-2x+4y-3=0$$ is
  • $$x^{2}+y^{2}-2x-4y+4=0$$
  • $$x^{2}+y^{2}+2x+4y-4=0$$
  • $$x^{2}+y^{2}-2x+4y+4=0$$
  • $$none\ of\ these$$
The length of the latus rectum of the parabola whose focus is $$\left ( 3,3 \right )$$ and directrix is  $$3x-4y-2=0$$ is
  • $$1$$
  • $$2$$
  • $$4$$
  • $$8$$
The triangle PQR is inscribed in the circle $$\displaystyle x^{2}+y^{2}= 25.$$ If $$Q$$ and $$R$$ have coordinates $$\displaystyle \left ( 3, 4 \right )$$ and $$\displaystyle \left ( -4, 3 \right ),$$ respectively, then $$\displaystyle \angle QPR$$ is equal to
  • $$\displaystyle \frac{\pi }{2}$$
  • $$\displaystyle \frac{\pi }{3}$$
  • $$\displaystyle \frac{\pi }{4}$$
  • $$\displaystyle \frac{\pi }{6}$$
The lines $$\displaystyle 2x - 3y = 5$$ and $$\displaystyle 3x - 4y = 7$$ intersect at the center of the circle whose area is $$154$$ sq. units, then equation of circle is
  • $$\displaystyle x^2 + y^2 - 2x + 2y = 47$$
  • $$\displaystyle x^2 + y^2 + 2x - 2y = 31$$
  • $$\displaystyle x^2 + y^2 - 2x - 2y = 47$$
  • $$\displaystyle x^2 + y^2 - 2x - 2y = 31$$
If the centroid of an equilateral triangle is $$(1, 1)$$ and its one vertex is $$(-1, 2)$$ then the equation of its circumcircle is
  • $$x^{2}+y^{2}-2x-2y-3=0$$
  • $$x^{2}+y^{2}+2x-2y-3=0$$
  • $$x^{2}+y^{2}+2x+2y-3=0$$
  • none of these
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