Locus of point of intersection of lines axsec θ + bytan θ = a and axtan θ + bysec θ = b , where

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10-2. Parabola, Ellipse, Hyperbola

easy

The locus of the point of intersection of the lines $ax\sec \theta + by\tan \theta = a$ and $ax\tan \theta + by\sec \theta = b$, where $\theta $ is the parameter, is

A

A straight line

B

A circle

C

An ellipse

D

A hyperbola

Solution

(d) Squaring and subtracting, we get

${a^2}{x^2} – {b^2}{y^2} = {a^2} – {b^2}$, which is the equation of hyperbola.

Standard 11

Mathematics

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