﻿ Let PQ be a diameter of the circle x2 + y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line,  x + y = 2 respectively, then the maximum value of αβ is ..... | Conic Section

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# Conic Section

#### Multiple Choice Questions

371.

The circle passing through the intersection of the circles, x2 + y2 – 6x = 0 and x+ y2 – 4y = 0, having its centre on the line, 2x – 3y + 12 = 0, also passes through the point :

• ( - 3, 6)

• ( - 3, 1)

372.

• 7x - 4y = 1

• 4x - 2y = 1

• 8x - 2y = 5

• 4x - 3y = 2

# 373.

Ans : 7

#### Multiple Choice Questions

374.

If the common tangent to the parabolas, y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2, then c is equal to :

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{2\sqrt{2}}$

• $\frac{1}{2}$

• $\frac{1}{4}$

375.

If the co–ordinates of two points A and B are  respectively and P is any point on the conic, 9x2 + 16y2 = 144, then PA + PB is equal to :

• 8

• 16

• 9

• 6

376.

If the line y = mx + c is a common tangent to the hyperbola

• 4c2 = 369

• 5m = 4

• c2 = 369

• 8m + 5 = 0

377.

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, the eccentricity e of the ellipse satisfies :

378.

The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is: