﻿ The locus of the foot of perpendicular drawn from the centre of the ellipse x2+3y2 =6 on any tangent to it is | Conic Section

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1.The locus of the foot of perpendicular drawn from the centre of the ellipse x2+3y2 =6 on any tangent to it is (x2-y2)2 = 6x2+2y2 (x2-y2)2 = 6x2 -2y2 (x2+y2)2 = 6x2+2y2 (x2+y2)2 = 6x2+2y2

C.

(x2+y2)2 = 6x2+2y2

Equation of ellipse is,

The slope of the perpendicular drawn from the centre (0,0) to (h,k) is k/h.
Since, both the lines are perpendicular,

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2.

The slope of the line touching both the parabolas y2 = 4x and x2-32y is

• 1/2

• 3/2

• 1/8

• 1/8

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3.

The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point

• (-5,2)

• (2,-5)

• (5,-2)

• (5,-2)

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4.

The equation of the circle passing through the foci of the ellipse  and having centre at (0,3) is

• x2+y2-6y-7 =0

• x2+y2-6y+7 =0

• x2+y2-6y-5 =0

• x2+y2-6y-5 =0

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5.

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 − Tn = 10, then the value of n is

• 7

• 5

• 10

• 10

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6.

Given A circle, 2x2 + 2y2= 5 and parabola,
Statement I An equation of a common tangent to these curves is
Statement II If the line  is the common tangent, then m satisfies m4-3m2+2 =0

• Statement I is true,  Statement II is true; Statement II is a correct explanation for statement I

• Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I

• Statement I is true, Statement II is false

• Statement I is true, Statement II is false

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7.

Statement I An equation of a common tangent to the parabola  and the ellipse 2x2 +y2 =4 is .
Statement II If the line  is a common tangent to the parabola  and the ellipse 2x2 +y2 =4, then m satisfies m4 +2m2 =24

• Statement 1 is false, statement 2 is true

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

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8.

The area bounded between the parabolas x2=y/4 and x2 = 9y, and the straight line y = 2 is

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9.

If z ≠ 1 and  is real, then the point represented by the complex number z lies

• either on the real axis or on a circle passing through the origin

• on a circle with centre at the origin

• either on the real axis or on a circle not passing through the origin

• either on the real axis or on a circle not passing through the origin

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10.

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) is

• 10/3

• 3/5

• 6/5

• 6/5

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