If a point P from where line drawn cuts coordinates axes at A and B (with A on x -axis and B on y -axis ) satisfies \alpha \frac{x^{2}}{P B^{2}} + \beta \frac{y^{2}}{P A^{2}} = 1, then \alpha + \beta is

Engineering

Mathematics

Line of Greatest Slope

Question

If a point

P

from where line drawn cuts coordinates axes at

A

and

B

(with

A

x -

axis and

B

y -

axis ) satisfies

α \frac{x^{2}}{P B^{2}} + β \frac{y^{2}}{P A^{2}} = 1

, then

α + β

1

2

3

4

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α \frac{x^{2}}{P B^{2}} + β \frac{y^{2}}{P A^{2}} = 1

P A = \sqrt{4 + 4} = 2 \sqrt{2}

P B = 2 \sqrt{2}

put value of

P A

P B

in given eqn

α \frac{4}{8} + β \frac{4}{8} = 1

α + β = 2

Option B

You can take any value of point

A

B

Answer will remain same.

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