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 , then α + β is

Engineering

Mathematics

Locus of a Point

Various Form of a Straight Line

Section Formulae and Centres of a Triangle

Question

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 $α \frac{x^{2}}{{PB}^{2}} + β \frac{y^{2}}{{PA}^{2}} = 1$ , then α + β is

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$α \frac{x^{2}}{{PB}^{2}} + β \frac{y^{2}}{{PA}^{2}} = 1$

PA = \sqrt{4 + 4} = 2 \sqrt{2}

PB = 2 \sqrt{2}

put value of PA & PB 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.