﻿ The line 3x + 2y + 1 = 0 meets the hyperbola 4x2 – y2 = 4a2 in the points P and Q. The coordinates of point intersection of the tangents at P and Qare : Kaysons Education

# The Line 3x + 2y + 1 = 0 Meets The Hyperbola 4x2 – y2 = 4a2 in The Points P and Q. The Coordinates Of Point Intersection Of The Tangents At P and Qare

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## Question

### Solution

Correct option is

(–3a2, 8a2)

According to give condition line ,

3x + 2y + 1 = 0                 …… (1)

Is chord of contact for hyperbola

4x2 – y2 = 4a2             …… (2)

Let (x1y1) be a point for which (1) is chord of contact.

Then by (2), 4xx1 – yy= 4a2           ……. (3)

Compare (1) and (3)

⇒ (–3a2, 8a2)

#### SIMILAR QUESTIONS

Q1

PN is the ordinate of any point P on the hyperbola  and AA’ is its transverse axis. If Q divides AP in the ratio a2 : b2, then NQ is

Q2

If SK perpendicular from focus S on th tangent at any point P of the hyperbola  , then K lies on

Q3

The lines 2x + 3y + 4 = 0 and 3x – 2y + 5 = 0 may be conjugate w.r.t. the hyperbola  if

Q4

The condition for two diameters of a hyperbola  represented by Ax2 + 2Hxy + By2 = 0 to be conjugate is

Q5

If the polars of (x1y1) and (x2y2) w.r.t. the hyperbola  are at right angles, then

Q6

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is

Q7

The number of tangents to the hyperbola  through (4, 3) is

Q8

The equation of the hyperbola referred to it axes as axes of coordinates whose latus rectum is 4 and eccentricity is 3, is

Q9

If a rectangular hyperbola whose center is C, is cut by any circle of radiusr in the four points P, Q, R, S, then

CP2 + CQ2 + CR2 + CS2 =

Q10

If θ is the angle between the asymptotes of the hyperbola   with eccentricity e, then