Important Questions of Conic Section Mathematics | Zigya

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301.

If y = 3x is a tangent to a circle with centre (1, 1), then the other tangent drawn through (0, 0) to the circle is

  • 3y = x

  • y = - 3x

  • y = 2x

  • y = - 2x


302.

The line among the following which touches the parabola y = 4ax, is

  • x + my + am2 = 0

  • x - my + am2 = 0

  • x + my - am2 = 0

  • y + mx + am2 = 0


303.

Which of the following equations gives a circle ?

  • r = 2sinθ

  • r2cos2θ = 1

  • r4cosθ + 5sinθ = 3

  • 5 = r1 + 2cosθ


304.

Let O be the origin and A be a point on the curve y = 4x. Then the locus of the mid point of OA is :

  • x2 = 4y

  • x2 = 2y

  • y2 = 16x

  • y2 = 2x


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305.

The number of common tangents to the two circles x2 + y - 8x + 2y = 0 and x2 + y2 - 2x - 16y + 25 = 0 is :

  • 1

  • 2

  • 3

  • 4


306.

Observe the following statements :

I. The circle x2 + y2 - 6x - 4y - 7 = 0 touches y-axis.

II. The circle x2 + y2 + 6x + 4y - 7 = 0 touches

x-axis. Which of the following is a correct statement ?

  • Both I and II are true

  • Neither I nor II is true

  • I is true, II is false

  • I is false, II is true


307.

The length of the tangent drawn to the circle x2 + y2 - 2x + 4y - 11 = 0

  • 1

  • 2

  • 3

  • 4


308.

If b and c are the lengths of the segments of any focal chord of a parabola y2 = 4ax, then the length of the semi-latus rectum is

  • bcb + c

  • bc

  • b + c2

  • 2bcb + c


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309.

Equations of the latus rectum of the ellipse

9x2 + 4y2 - 18x - 8y - 23 = 0 are : 

  • y = ± 5

  • x = ± 5

  • y = 1 ± 5

  • x = - 1 ± 5


310.

If the eccentricity of a hyperbola is 3; then the eccentricity of its conjugate hyperbola is :

  • 2

  • 3

  • 32

  • 23


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