Question

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

Solution

Correct option is

2x + 3y + 4 = 0               ….. (1),   

3x – 2y + 5 = 0                …. (2)

Are conjugate lines w.r.t. hyperbola

                    …. (3)

Let (x1y1) be pole of line (1) w.r.t. (3). Then its polar is

                 …. (4)

Compare (1) and (4), 

     

.

By assumption (1) and (2) are conjugate, so pole of line (1) lies on (2)

⇒ 3x1 – 2y+ 5 = 0

⇒ 3a2 + 3b2 = 10

SIMILAR QUESTIONS

Q1

If the polar of a point with respect to  toches the hyperbola , then the locus of the point is

Q2

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Q3

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Q4

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Q5

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Q6

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Q7

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

Q8

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

Q9

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 and Qare

Q10

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