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CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 9 - MCQExams.com

Find the equation of a circle whose centre is (2, - 1 ) an radius is 3
  • x2+y2+4x2y+4=0
  • x2+y24x+2y4=0
  • x2+y2+4x+2y4=0
  • x2+y2+2x4y4=0
The equation of a circle which is passing through the vertices of an equilateral triangle whose median is of length 3 a is
  • x2+y2=9a2
  • x2+y2=16a2
  • x2+y2=4a2
  • x2+y2=a2
Equation (x2)2+y2+(x+2)2+y2 = 4 represents _____________.
  • Parabola
  • Ellipse
  • Circle
  • straight lines
If |zz0|=|a¯z+a¯z+b|2|a| represent a parabola, Then the  length of latus  rectum of parabola 
  • |a¯z0¯az0+b|
  • |a¯z0¯az0+b||a|
  • |a¯z0¯az0+b|2|a|
  • None of these
If the tangent to the curve, y=x3+axb at the point (1,5) is perpendicular to the line, x+y+4=0, then which one of the following points lies on the curve?
  • (2,2)
  • (2,2)
  • (2,1)
  • (2,1)
In what ratio, the point of intersection of the common tangents to hyperbola x21y28=1 and parabola y2=12x, divides the foci of the given hyperbola?
  • 3:4
  • 3:2
  • 5:4
  • 5:3
AB is a chord of the circle x2+y2=9. The tangent at A and B intersect at C. If (1,2) is the midpoint of AB, the area of ABC is (in square units).
  • 9
  • 75
  • 95
  • 85
The equation x22λ+y2λ51=0 represents an ellipse, if
  • λ<5
  • λ<2
  • 2<λ<5
  • λ<2 or λ<5
The eccentricity of the ellipse 5x2+9y2=1 is
  • 23
  • 34
  • 45
  • 12
The eccentricity of the ellipse 9x2+25y218x100y116=0, is
  • 25/16
  • 4/5
  • 16/25
  • 5/4
An ellipse has its centre at (1,1) and semi-major axis =8 and it passes through the point (1,3). The equation of the ellipse is
  • (x+1)264+(y+1)216=1
  • (x1)264+(y+1)216=1
  • (x1)216+(y+1)264=1
  • (x+1)264+(y1)216=1
The eccentricity of the ellipse 25x2+162=400 is
  • 35
  • 13
  • 25
  • 15
Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.
  • 13
  • 15
  • 12
  • None of the above
If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to
  • 13
  • 13
  • 12
  • 223
  • 232
If the latus-rectum of an ellipse is one half of its minor axis, then its eccentricity is
  • 12
  • 12
  • 32
  • 34
The eccentricity of the conic 9x2+25y2=225 is
  • 25
  • 45
  • 13
  • 15
  • 35
The vertex of the parabola y24yx+3=0 is
  • (1,3)
  • (1,2)
  • (2,1)
  • (3,1)
The eccentricity of the conic 9x216y2=144 is
  • 54
  • 43
  • 45
  • 7
 The equation 5x2+y2+y=8 represents 
  • An ellipse
  • A parabola
  • A hyperbola
  • A Circle
Write the length of the latus-rectum of the hyperbola 16x29y2=144
  • 53
  • 43
  • 34
  • 45
The equation of the circle with centre (2,2) which passes through (4,5) is 
  • x2+y24x+4y77=0
  • x2+y24x4y5=0
  • x2+y2+2x+2y59=0
  • x2+y22x2y23=0
  • x2+y2+4x2y26=0
The centre of the ellipse 4x2+y28x+4y8=0 is
  • (0,2)
  • (2,1)
  • (2,1)
  • (1,2)
The latus-rectum of the hyperbola 16x49y2=144 is
  • 16/3
  • 32/3
  • 8/3
  • 4/3
The eccentricity of the ellipse (x1)22+(y+34)2=116 is
  • 12
  • 122
  • 12
  • 14
The latus rectum of the parabola x=at2+bt+c,y=at2+bt+c is
  • (aabb)2(a2+a2)32
  • (abab)2(a2+a2)32
  • (bbaa)2(b2+b2)32
  • (abab)2(b2+b2)32
The foci of the ellipse 25(x+1)2+9(y+2)2=225, are at
  • (1,2) and (1,6)
  • (2,1) and (2,6)
  • (1,2) and (2,1)
  • (1,2) and (1,6)
The centre of a circle is C(2,5) and the circle passes through the point A(3,2). The equation of the circle is
  • x2+y24x+10y21=0
  • x2+y2+4x+6y21=0
  • x2+y2+4x10y+21=0
  • none of these
If the parabola y2=4ax passes through the point P(3,2), then the length of its latus rectum is
  • 13
  • 23
  • 43
  • 4
The equation ax2+4xy+y2+ax+3y+2=0 represents a parabola if a is
  • 4
  • 4
  • 0
  • 8
The latus rectum of the hyperbola 9x216y218x32y151=0 is 
  • 94
  • 9
  • 32
  • 92
If the eccentricity of the ellipse x2a2+1+y2a2+2=1is16 , then latus rectrum of ellipse is 
  • 56
  • 106
  • 86
  • none of these
The co- ordinates (2,3) and (1,5)are the foci of an ellipse which passes through the origin , then the equation of 
  • tangent at the origin is (325)x+(122)y=0
  • tangent at the origin is (32+5)x+(1+22y)=0
  • normal at the origin is (32+5)x(22+1)y=0
  • normal at the origin is x(325)y(122)=0
If the equation of the ellipse is 3x2+2y2+6x8y+5=0, then which of the following is/ are true?
  • e=13
  • center is (-1,2)
  • foci are (-1,1) and (-1,3)
  • directrices are y=2±3
Consider the parabola whose focus is at (0,0) and tangent at vertex is xy+1=0

The length of latus rectum is
  • 42
  • 22
  • 82
  • 32
The length of the latus rectum of the parabola whose focus is (u22gsin2α,u22gcos2α) and directrix is y=u22g is 
  • u22gcos2α
  • u22gcos2α
  • 2u22gcos2α
  • 2u22gcos2α
The centre of a circle whose end points of a diameter are (6,3) and (6,4) is
  • (8,1)
  • (4,7)
  • (0,72)
  • (4,72)
The graph of y=x2 is a straight line.
  • True
  • False
If (0, 0) be the vertex and 3x4y+2=0 be the directrix of a parabola,
 then the length of its latus rectum is - 
  • 45
  • 25
  • 85
  • 15
The distance between the foci of an ellipse is 16 and eccentricity is \dfrac12. Length of the major axis of the ellipse is
  • 8
  • 64
  • 16
  • 32
\text{The length of the latus rectum of the parabola } x= ay^2+by+c \text{ is -}
  • \dfrac{a}{4}
  • \dfrac{a}{3}
  • \dfrac{1}{a}
  • \dfrac{1}{4a}
The hyperbola \dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1 has its conjugate axis of length 5 and passes through the point (2, 1). The length of latus rectum is :
  • \dfrac{5}{4}\sqrt{29}
  • \dfrac{5}{8}\sqrt{29}
  • \sqrt{29}
  • \dfrac{\sqrt{29}}{4}
The graph of the curve x^2 + y^2 - 2xy - 8x - 8y + 32 = 0 falls wholly in the
  • first quadrant
  • second quadrant
  • third quadrant
  • none of these
f(\displaystyle \mathrm{m}_{\mathrm{i}}, \frac{1}{\mathrm{m}_{\mathrm{i}}}) , \mathrm{i}=1,2,3,4 are four distinct points on the circle with centre origin, then value of \mathrm{m}_{1}\mathrm{m}_{2}\mathrm{m}_{3}\mathrm{m}_{4} is equal to
  • 0
  • -1
  • 1
  • -a^{2}
lf the equation 136 (x^{2}+y^{2})=(5x+3y+7)^{2} represents a conic, then its length of latus rectum is
  • \displaystyle \frac{7}{2\sqrt{34}}
  • \displaystyle \frac{7}{\sqrt{34}}
  • \displaystyle \frac{14}{\sqrt{34}}
  • \displaystyle \frac{9}{\sqrt{34}}
A point P(x, y) moves in XY plane such that x = a\cos^2 \theta and y = 2a \sin \theta, where \theta is a parameter. The locus of the point P is
  • circle
  • ellipse
  • unbounded parabola
  • part of a parabola
Let P point on the circle x^2 + y^2 = 9, Q a point on the line 7x + y + 3 = 0, and the perpendicular bisector of PQ be the line x - y + 1 = 0. Then the coordinate of P are
  • (0, -3)
  • (0, 3)
  • \displaystyle \left ( \frac{72}{25}, -\frac{21}{25} \right)
  • \displaystyle \left ( -\frac{72}{25}, \frac{21}{25} \right)
The length of latus rectum of the parabola whose parametric equations are x = t^{2} + t + 1, y = t^{2}-  t + 1, where t \in R, is equal to?
  • \sqrt{2}
  • \sqrt{4}
  • \sqrt{8}
  • \sqrt{6}
For the variable, the locus of the point of intersection of the lines 3tx-2y+6t=0 and 3x+2ty-6=0 is
  • the ellipse \cfrac { { x }^{ 2 } }{ 4 } +\cfrac { { y }^{ 2 } }{ 9 } =1
  • the ellipse \cfrac { { x }^{ 2 } }{ 9 } +\cfrac { { y }^{ 2 } }{ 4 } =1
  • the hyperbola \cfrac { { x }^{ 2 } }{ 4 } -\cfrac { { y }^{ 2 } }{ 9 } =1
  • the hyperbola \cfrac { { x }^{ 2 } }{ 9 } -\cfrac { { y }^{ 2 } }{ 4 } =1
If the line 3x+4y=24 and 4x+3y=24 intersects the coordinates axes at A,B,C and D, then the equation of the circle passing through these 4 points  is
  • x^{2}+y^{2}-12x-12y+48=0
  • x^{2}+y^{2}-14x-14y+48=0
  • x^{2}+y^{2}-12x-12y+46=0
  • x^{2}+y^{2}-14x-14y+46=0
The equation of a straight line drawn through the focus of the parabola y^2=-4x at an angle of 120^o to the x-axis is.
  • y+\sqrt 3(x-1)=0
  • y-\sqrt 3(x-1)=0
  • y+\sqrt 3(x+1)=0
  • y-\sqrt 3(x+1)=0
0:0:2


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