CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 6 - MCQExams.com

If a be the radius of a circle which touches x-axis at the origin, then its equation is

  • $${ x }^{ 2 }+{ y }^{ 2 }+ax=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }\pm 2ya=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }\pm 2xa=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+ya=0$$
The centre of the circle $$(x-a)(x-b)+(y-c)(y-c)=0$$ is 
  • $$(a+b,c+d)$$
  • $$9-a-b,-c-d)$$
  • $$\left(\dfrac{a+b}{2},\dfrac{c+d}{2}\right)$$
  • none of these
Cantres of the three circles
$$x^{2}+y^{2}-4x-6y-14=0$$
$$x^{2}+y^{2}+2x+4y-5=0$$
and $$x^{2}+y^{2}-10x-16y+7=0$$
  • Are the vertices of a right triangle
  • The vertices of an isosceles triangle which is not regular
  • Vertices of a regular triangle
  • Are collinear
Equation of the circle with centre on the $$y-$$axis and passing through the origin and the point $$(2,3)$$ is
  • $$x^{2}+y^{2}+13y=0$$
  • $$3x^{2}+3y^{2}+13x+3=0$$
  • $$6x^{2}+6y^{2}-13y=0$$
  • $$x^{2}+y^{2}+13+3=0$$
If the vertex $$= (2, 0)$$ and the extremities of the latus rectum are $$(3, 2)$$ and $$(3, -2)$$, then the equation of the parabola is 
  • $$y^2 = 2x - 4$$
  • $$x^2 = 4y - 8$$
  • $$y^2 = 4x - 8$$
  • None
The graph of curve 
$${x^2} + {y^2} - 8x - 8y + 32 = 0$$ falls wholly in the
  • first quadrant
  • second quadrant
  • third quadrant
  • none of these
The eccentricity of the hyperbola whose latus-return is $$8$$ and length of the conjugate axis is equal to half the distance between the foci, is
  • $$\dfrac43$$
  • $$\dfrac4{\surd 3}$$
  • $$\dfrac2{\surd 3}$$
  • $$None\ of\ these$$
If $$(4,3)$$ and $$(-12,-1)$$ are end points of a diameter of a circle, then the equation of the circle is-
  • $${ x }^{ 2 }+{ y }^{ 2 }-8x-2y-51=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+8x-2y-51=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+8x+2y-51=0$$
  • None of these
if the lines $$ 3x-4y-7=0$$ and $$2x-3y-5=0$$ are two diameter of a circle of area $$49\pi$$ square units the equation of the circle is
  • $$ x^2+y^2+2x-2y-62=0$$
  • $$ x^2+y^2-2x+2y-62=0$$
  • $$ x^2+y^2-2x+2y-47=0$$
  • $$ x^2+y^2+2x-2y-47=0$$
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $$ (-3,1)$$ and has eccentricity $$\sqrt {\frac{2}{5}} $$ is 
  • $$5x^3+3y^2-48=0$$
  • $$3x^2+5y^2-15=0$$
  • $$5x^2+3y^2-32=0$$
  • $$3x^2+5y^2-32=0$$
The name of the conic represented by $$\sqrt{\dfrac{x}{a}}+\sqrt{\dfrac{y}{b}}=1$$ is
  • Circle
  • Parabola
  • Ellipse
  • Hyperbola
The ellipse $$\dfrac{{{x^2}}}{{{a^2}}} + \dfrac{{{y^2}}}{{{b^2}}} = 1$$ cuts x axis at A and y axis at B and the line joining the focus S and B makes an angle $$\dfrac{{3\pi }}{4}$$ with x-axis. Then the eccentricity of the ellipse is 
  • $$\dfrac{1}{{\sqrt 2 }}$$
  • $$\dfrac{1}{2}$$
  • $$\dfrac{{\sqrt 3 }}{2}$$
  • $$\dfrac{1}{3}$$
The equation of the tangent to the ellipse such that sum of perpendiculars dropped from foci is 2 units, is
  • $$y cos3\pi/ 4 - x sin 3\pi /4=1$$
  • $$y sin \frac{3\pi}{8}- x cos \frac{3\pi}{8}=1$$
  • $$x cos \pi /8 - sin \pi /8=1$$
  • $$y cos \frac{5\pi}{8}+x sin \frac{5\pi}{8}=1$$
$$(a, c)$$ and $$(b, c)$$ are the centres of two circles whose radical axis is the y-axis. If the radius of first circle is $$r$$ then the diameter of the other circle is 
  • $$2\sqrt {{r^2} - {b^2} + {a^2}} $$
  • $$\sqrt {{r^2} - {a^2} + {b^2}} $$
  • $$\left( {{r^2} - {b^2} + {a^2}} \right)$$
  • $$2\sqrt {{r^2} - {a^2} + {b^2}} $$
The equation of the latus rectum of the hyperbola $$\dfrac{(x-4)^2}{16}-\dfrac{(y-3)^2}{20}=1$$ are?
  • $$x=1\pm 5$$
  • $$x=4\pm 6$$
  • $$y=2\pm 6$$
  • $$y=3\pm 5$$
The locus of the mid point of the focal radii of a variable point moving on the parabola, $${y^2}={8x}$$ is a parabola whose
  • Latus rectum is half the latus rectum of the original parabola
  • Vertex is $$(1,0)$$
  • Directrix is $$y-axis$$
  • Focus has the co-ordinates $$(2,0)$$
Equation of circle having centre $$(5, 2)$$ and which passes through the point $$(1, -1)$$ is?
  • $$x^2+y^2-10x-4y-4=0$$
  • $$x^2+y^2+10x+4y+4=0$$
  • $$x^2+y^2-10x-4y-2=0$$
  • $$x^2+y^2-10x-4y+4=0$$
$${x^2} - {y^2} + 5x + 8y - 4 = 0$$
  • rectangular hyperbola
  • ellipse
  • hyperbola
  • pair of lines
S and S' foci of an ellipse. B is one end of the minor axis. If $$\angle{SBS'}$$ is a right angled isosceles triangle, then e$$=?$$
  • $$\dfrac{1}{\sqrt{2}}$$
  • $$\dfrac{1}{2}$$
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$\dfrac{3}{4}$$
The latusrectum of a parabola $$y^{2}=4ax$$ whose focal chord is $$PSQ$$ such that $$SP=3$$ and $$SQ=2$$, is given by
  • $$\dfrac{24}{5}$$
  • $$\dfrac{12}{5}$$
  • $$\dfrac{6}{5}$$
  • $$\dfrac{1}{5}$$
If the focus of a parabola divided a focal chord of the parabola in segment of length $$3$$ and $$2$$ the length of the latus rectum of the parabola is ?
  • $$\dfrac{3}{2}$$
  • $$\dfrac{6}{5}$$
  • $$\dfrac{12}{5}$$
  • $$\dfrac{24}{4}$$
Equation of the circle with radius 3 and centre as the point of intersection of the lines $$2x + 3y = 5, 2x - y = 1$$ is 
  • $$x^2 + y^2 = 9 $$
  • $$x^2 + y^2 - 2x - 2y - 7 = 0 $$
  • $$x^2 + y^2 - 2x - 2y + 7 = 0$$
  • $$x^2 + y^2 + 9 = 0$$
A square is inscribed in the circle $$x^2 +y^2 - 4x - 6y-5 =0$$ whose sides are parallel to co-ordinate axes then vertices of square are 
  • $$ (5, 0), (5, 6), (-1, 0), (-1, 6) $$
  • $$(5, 1), (5,-6), (-1, 1), (-1, 6)$$
  • $$ (5, 1), (5, 6), (-1, 0), (1, 6) $$
  • $$ (0, 5), (-6, 5), (0,-1),(6, 1) $$
If the lines $$3x-4y-7=0$$ and $$2x-3y-5=0$$ are two diameters of a circle of area 154 square units , the equation of the circle is :
  • $$x^2+y^2+2x-2y-62=0$$
  • $$x^2+y^2-2x+2y-62=0$$
  • $$x^2+y^2-2x+2y-47=0$$
  • $$x^2+y^2+2x-2y-47=0$$
The lines $$2x - 3y = 5$$ and $$3x - 4y = 7$$ are two diameters of a circel of area $$154sq.$$ units. Then the equation of circle is
  • $$(x+1)^2+(y+1)^2 = 49$$
  • $$(x-1)^2 + (y-1)^2=-49$$
  • $$(x-1)^2+(y+1)^2 = 49$$
  • $$(x+1)^2+(y-1)^2 = 49$$
A variable point $$P$$ on the ellipse of eccentricity is joined to the foci $$S$$ and $$s'$$. The eccentricity of the locus of the in cetre of the triangle $$PSS^{1}$$ is
  • $$\sqrt {\dfrac {2e}{1+e}}$$
  • $$\sqrt {\dfrac {e}{1+e}}$$
  • $$\sqrt {\dfrac {1-e}{1+e}}$$
  • $$\dfrac {e}{2(1+e)}$$
The circles $${x}^{2}+{y}^{2}-4x+4y+4=0$$ and $${x}^{2}+{y}^{2}-4x-4y=0$$
  • Do not intersect
  • Are not orthogonal
  • Intersect orthogonally
  • Concentric
The set of values of p for which the power of a point $$(2,5)$$ is negative with respect to a circle $${ x }^{ 2 }+{ y }^{ 2 }-8x-12y+p=0$$ which neither touches the axes nor cuts them are
  • (36,57)
  • (36,47)
  • (37,47)
  • (16,47)
If focus of the parabola is $$(3,0)$$ and length of latus rectum is $$8$$, then its vertex is
  • $$(2,0)$$
  • $$(1,0)$$
  • $$(0,0)$$
  • $$(-1,0)$$
If the equation $$ax^{2}+2(a^{2}+ab-16)xy+by^{2}2ax+2by-\sqrt[4]{2}=0$$ represents a circle, the radius of the circle is 
  • $$\sqrt{16 + \sqrt[4]{2}}$$.
  • $$\sqrt{24 + \sqrt[4]{2}}$$.
  • $$\sqrt{2}$$
  • $$\sqrt[4]{2}$$
A circle has radius $$3$$ units and its centre lies on the line $$y=x-1$$. if it passes through $$(7,3)$$, its equation
  • $$x^{2}+y^{2}-8x-14y=0$$
  • $$x^{2}+y^{2}-8x-6y-6=0$$
  • $$x^{2}+y^{2}-14x-12y-76=0$$
  • $$x^{2}+y^{2}+14x+12x-70=0$$
Two rods of lengths 'a' and 'b' slide along coordinate aces such that their ends are concyclic. Locus of the centre of the circle is?
  • $$4(x^2+y^2)=a^2+b^2$$
  • $$4x(x^2+y^2)=a^2-b^2$$
  • $$4(x^2-y^2)=a^2-b^2$$
  • $$xy=ab$$
The length of the diameter of the circle which touches the $$x-$$axis at the point $$(1,0)$$ and passes through the point $$(2,3)$$
  • $$6/5$$
  • $$5/3$$
  • $$10/3$$
  • $$3/5$$.
$$P$$ and $$Q$$ are any two points on the circle $$x^2 + y^2 = 4$$ such that $$PQ$$ is a diameter. If $$\alpha$$ and $$\beta$$ are the lengths of perpendicular from $$P$$ and $$Q$$ on $$x + y = 1$$ then the maximum value of $$\alpha \beta$$ is
  • $$\dfrac{1}{2}$$
  • $$\dfrac{7}{2}$$
  • $$1$$
  • $$2$$
The circle passing through the points $$(-1,0)$$ and touching the y-axis at $$(0,2)$$ also passes through the point:
  • $$(-\dfrac{3}{2},0)$$
  • $$(-\dfrac{5}{2},2)$$
  • $$(-\dfrac{3}{2},\dfrac{5}{2})$$
  • $$(-4,0)$$
The equation of the circle passing through $$(3, 6)$$ and whose centre is $$(2, -1)$$ is
  • $$x^{2}+y^{2}-4x+2y=45$$
  • $$x^{2}+y^{2}-4x-2y+45=0$$
  • $$x^{2}+y^{2}+4x-2y=45$$
  • $$x^{2}+y^{2}-4x+2y+45=0$$
If $$(6, -3)$$ is the one extremity of diameter to the circle $$x^{2}+y^{2}-3x+8y-4=0$$ then its other extremity is-
  • $$(3/2, -4)$$
  • $$(-3, -5)$$
  • $$(3, -5)$$
  • $$(3, 5)$$
The equation of circle with centre $$(1,2)$$ and tangent $$x+y-5=0$$ is
  • $${x}^{2}+{y}^{2}+2x-4y+6=0$$
  • $${x}^{2}+{y}^{2}-2x-4y+3=0$$
  • $${x}^{2}+{y}^{2}-2x+4y+8=0$$
  • $${x}^{2}+{y}^{2}-2x-4y+8=0$$
Eccentricity of an ellipse is $$\sqrt {\cfrac{2}{5}} $$ and it passes through the point $$(-3,1)$$ then its equation is 
  • $$3{x^2} + 5{y^2} = 32$$
  • $$2{x^2} + 3{y^2} = 33$$
  • $$3{x^2} + 4{y^2} = 30$$
  • $$2{x^2} + 3{y^2} = 34$$
The equation of the circle having the lines $$y^{2}+2y+4x-2xy=0$$ as its normals & passing through the point$$(2,1)$$ is
  • $$x^{2}+y^{2}-2x-4y+3=0$$
  • $$x^{2}+y^{2}-2x+4y+3=0$$
  • $$x^{2}+y^{2}-2x+4y-5=0$$
  • $$x^{2}+y^{2}+2x+4y+13=0$$
The circle $${x^2} + {y^2} - 3x - 4y + 2 = 0$$ cuts $$x$$-axis
  • $$(2,0),(-3,0)$$
  • $$(3,0),(4,0)$$
  • $$(1,0),(-1,0)$$
  • $$(1,0),(2,0)$$
What is the area enclosed by $$|x|+|y|=1$$ ?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Equation of the circle which passes through the centre of the circle $$x^{2} + y^{2} + 8x + 10y - 7 = 0$$ and is concentric with the circle $$2x^{2} + 2y^{2} - 8x - 12y - 9 = 10$$ is
  • $$x^{2} + y^{2} - 4x - 8y - 97 = 0$$
  • $$x^{2} + y^{2} - 4x - 6y - 87 = 0$$
  • $$x^{2} + y^{2} - 2x - 8y - 95 = 0$$
  • None of these
The centres of a set of circles, each of radius $$3$$, lie on the circle $${x}^{2}+{y}^{2}=25$$. The lotus of any point in the set is 
  • $$4\le {x}^{2}+{y}^{2}\le 64$$
  • $${x}^{2}+{y}^{2}\le 25$$
  • $${x}^{2}+{y}^{2}\ge 25$$
  • $$3\le {x}^{2}+{y}^{2}\le 9$$
 The curve described parametrically by$$x = {t^2} + t + 1$$ and $$y = {t^2} - t + 1$$ represents 
  • hyperbola
  • ellipse
  • parabola
  • rectangular hyperbola
If $$2x - 3y = 5$$ and $$3x - 4y = 7$$ are the equation of $$2$$ diameters of a circle whose area is $$88$$ sq. units then the equation of the circle is :
  • $${x^2} + {y^2} + 2x - 2y - 47 = 0$$
  • $${x^2} + {y^2} - 2x + 2y - 49 = 0$$
  • $${x^2} + {y^2} - 2x + 2y + 47 = 0$$
  • $${x^2} + {y^2} - 2x + 2y - 26 = 0$$
If he equations of two diameters of a circle are $$2x + y = 6$$ and $$3x + 2y = 4$$ and the radius is $$10$$ , find the equation of the circle. 
  • $$x^{2}+y^{2}-16x+20y+64=0$$
  • $$x^{2}-y^{2}+16x-20y+34=0$$
  • $$x^{2}+y^{2}+6x-20y+64=0$$
  • None of these
The equation $$\dfrac{{x}^{2}}{2-r}+\dfrac{{y}^{2}}{r-5}+1=0$$ represents an ellipse if
  • $$r>1$$
  • $$r>5$$
  • $$2 < r< 5$$
  • $$r<2$$ or $$r>5$$
The equation of directrix of a parabola $$3 x + 4 y + 15 = 0$$ and equation of tangent at vertex is $$3 x + 4 y - 5 = 0$$ . Then the length of latus rectum is equal to- 
  • 15
  • 14
  • 13
  • 16
Which of the following equations represents parametrically, parabolic profile ?
  • $$x=3\:cos\:t\:;\:y=4\:sin\:t$$
  • $$x^2-2=-\:cos\:t\:;\:y=4\:cos^2\:\dfrac{t}{2}$$
  • $$\sqrt{x}=tan\:t\:;\:\sqrt{y}=sec\:t$$
  • $$x=\sqrt{1-sin\:t};\:y=sin\:\dfrac{t}{2}+cos\:\dfrac{t}{2}$$
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