﻿ 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 | Conic Section

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# Conic Section

#### Multiple Choice Questions

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

659 Views

2.

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

• 1/2

• 3/2

• 1/8

• 1/8

398 Views

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)

181 Views

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

225 Views

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

266 Views

# 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

B.

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

Equation of circle can be rewritten as,
x2 +y2 = 5/2
Let common tangent be

The perpendicular from centre to the tangent is equal to radius,
therefore,

thus, both Statements are correct.

238 Views

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

197 Views

8.

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

721 Views

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

159 Views

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

172 Views