Question

lf P is a point lying on x^2/16 + y^2/9 = 1 and A( √7, 0) B(√7, 0) are two points then PA +PB = ?

Answer 1

ANSWER.

=> PA + PB = 8

EXPLANATION.

$\sf \to \: if \: p \: lying \: on \: equation \: = \dfrac{ {x}^{2} }{16} + \dfrac{ {y}^{2} }{9} = 1 \\ \\ \sf \to \: two \: points \: are \: \: a( \sqrt{7},0) \: \: and \: \: \: b( - \sqrt{7} ,0) \: are \: two \: \: points$

$\sf \to \: {a}^{2} = 16 \\ \\ \sf \to \: {b}^{2} = 9 \\ \\ \sf \to \: formula \: of \: eccentricity \: \implies \: {b}^{2} = {a}^{2} (1 - {e}^{2} ) \\ \\ \sf \to \: 9 = 16(1 - {e}^{2} ) \\ \\ \sf \to \: 9 = 16 - 16 {e}^{2} \\ \\ \sf \to \: {e}^{2} = \dfrac{7}{16} \\ \\ \sf \to \: e \: = \frac{ \sqrt{7} }{4} = answer$

$\sf \to \: as \: we \: can \: find \: their \: focus \: \implies \: (ae,0) \: \: and \: \: ( - ae,0) \\ \\ \sf \to \: a \: = 4 \implies \: (4 \times \frac{ \sqrt{7} }{4} ,0) \: \: and \: \: ( - 4 \times \frac{ \sqrt{7} }{4} ,0) \\ \\ \sf \to \: focus \: = ( \sqrt{7} ,0) \: \: \: and \: \: \: ( - \sqrt{7} ,0) \\ \\ \sf \to \: pa \: + \: pb \: = length \: of \: major \: axis$

$\sf \to \: length \: of \: major \: axis \: = 2a \: = 2 \times 4 = 8 \\ \\ \sf \to \: { \underline{option \: (3) \: \: is \: \: correct}}$