Important Questions of Conic Section Mathematics | Zigya

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221.

The equation of the tangents of hyperbola 3x2 - 4y2 = 12 which cuts equal intercepts from both the axes, are

  • y + x = ± 1

  • x - y = ± 1

  • y - x = ± 1

  • 4y - 3x = 0


222.

Equation of the tangent to the hyperbola 2x2 - 3y2 = 6. Which is parallel to the line y - 3x - 4 = 0 is

  • y = 3x + 8

  • y = 3x - 8

  • y = 3x + 2

  • None of these


223.

The equation of circle which touches the axes and the line and whose centre lies inthe first quadrant is x2 + y2 - 2cx - 2cy + c2 = 0. Then, c is equal to

  • 1

  • 2

  • 3

  • 6


224.

The equation of the parabola having the focus at the point (3, - 1) and the vertex at (2, - 1)is

  • y2 - 4x - 2y + 9 = 0

  • y2 + 4x + 2y - 9 = 0

  • y2 - 4x + 2y + 9 = 0

  • y2 + 4x - 2y + 9 = 0


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225.

Find the equation of tangents to the ellipse x2a2 + y2b2 = 1 which cut off equal intercepts on the axes.

  • y = 3x ± 3a2 + b2

  • y = ± x  a2 + b2

  • y = 3x ± a2 + 3b2

  • None of the above


226.

The locus ofthe point of intersection of the lines xcosα + ysinα = p and xsinα - ycosα = q (α is a variable) will be

  • a circle

  • a staright line

  • a parabola

  • an ellipse


227.

The locus of the mid points of the chords of a circle which subtend a right angle at its centre (equation ofthe circle is x2 + y2 = a2)will be

  • x2 + y2 = 3a2

  • x2 + y2a23

  • 2(x2 + y2) = a2

  • 4(x2 + y2) = a2


228.

If the line 3x - 2y + p = 0 is normal to the circle x2 + y2 = 2x - 4y - 1, then p will be

  • - 5

  • 7

  • - 7

  • 5


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229.

If the two circles x2 + y2 = r2 and x2 + y2 - 10x + 16 = 0 intersect at two real points, then

  • 1 < r < 7

  • 3 < r < 10

  • 2 < r < 9

  • 2 < r < 8


230.

The equation of the common tangent to the parabolas y2 = 2x and x2 = 16y will be

  • x + y + 2 = 0

  • x - 3y + 1 = 0

  • x + 2y - 2 = 0

  • x + 2y + 2 = 0


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