Important Questions of Conic Section Mathematics | Zigya

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371.

If a = 9 is a chord of contact of the hyperbola x2 - y2 = 9, then the equation of the tangent at one of the points of contact is 

  • x + 3y + 2 = 0

  • 3x + 22y - 3 = 0

  • 3x - 2y + 6 = 0

  • x - 3y + 2 = 0


372.

The area (in sq units) bounded by the curves x = - 2y2 and x = 1 - 3y2 is

  • 23

  • 1

  • 43

  • 53


373.

A circle with centre at (2, 4) is such that the line x + y + 2 = 0 cuts a chord of length 6. The radius of the circle is

  • 41 cm

  • 11 cm

  • 21 cm

  • 31 cm


374.

The point at which the circles x2 + y2 - 4x - 4y + 7 = 0 and x2 + y2 - 12x - 10y + 45 = 0 touch each other, is

  • 135, 145

  • 25, 56

  • 145, 135

  • 125, 2 + 215


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375.

The length of the common chord of the two circles x2 + y2 - 4y = 0 and x2 + y2 - 8x - 4y + 11 = 0, is

  • 1454 cm

  • 112 cm

  • 135 cm

  • 1354


376.

The locus of the centre of the circle, which cuts the circle x2 + y2 - 20 + 4 = 0 orthogonally and touches the line x = 2, is

  • x2 = 16y

  • y2 = 4x

  • y2 = 16x

  • x2 = 4y


377.

If a normal chord at a point t on the parabola y2 = 4ax subtends a right angle at the vertex, then t equals to

  • 1

  • 2

  • 2

  • 3


378.

The slopes of the focal chords of the parabola y2 = 32x, which are tangents to the circle x2 + y2 = 4, are

  • 12, - 12

  • 13, - 13

  • 115, - 115

  • 25, - 25


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379.

If tangents are drawn from any point on the circle x2 + y= 25 to the ellipse x216 + y29 = 1,  then the angle between the tangents is

  • 2π3

  • π4

  • π3

  • π2


380.

An ellipse passing through has 42, 26 foci at (- 4, 0) and (4, 0). Then, its eccentricity

  • 2

  • 12

  • 12

  • 13


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