Question-58652

Question Number 58652 by peter frank last updated on 27/Apr/19

Commented by peter frank last updated on 27/Apr/19

a a n d b

Answered by tanmay last updated on 27/Apr/19

A P i s (y - 0) = m (x - 5)

B Q i s (y - 0) = m (x + 5)

s o l v e y = m (x - 5) a n d 4 x + 3 y = 25 t o f i n d P

4 x + 3 m (x - 5) = 25

4 x + 3 m x - 15 m = 25

x = \frac{25 + 15 m}{4 + 3 m} a n d y = m (\frac{25 + 15 m}{4 + 3 m} - 5)

= m (\frac{25 + 15 m - 20 - 15 m}{4 + 3 m})

= (\frac{5 m}{4 + 3 m})

s o P (\frac{25 + 15 m}{4 + 3 m}, \frac{5 m}{4 + 3 m})

n o w s o l v e y = m (x + 5) a n d 4 x + 3 y = 25 t o f i n d Q

4 x + 3 m (x + 5) = 25

4 x + 3 m x + 15 m = 25

x = \frac{25 - 15 m}{4 + 3 m}, y = m (\frac{25 - 15 m}{4 + 3 m} + 5)

Q (\frac{25 - 15 m}{4 + 3 m}, (\frac{25 - 15 m + 20 + 15 m}{4 + 3 m}) \times m

(\frac{25 - 15 m}{4 + 3 m}, \frac{45 m}{4 + 3 m})

P Q = \sqrt{{(_{} \frac{25 + 15 m}{4 + 3 m}) -_{} (\frac{25 - 15 m_{}}{4 + 3 m})}^{2} + {(\frac{45 m - 5 m}{4 + 3 m})}^{2}}

= \sqrt{\frac{900 m^{2}}{{(4 + 3 m)}^{2}} + \frac{1600 m^{2}}{{(4 + 3 m)}^{2}}} = 5

\frac{50 m}{4 + 3 m} = 5

50 m - 15 m = 20

m = \frac{20}{35} = \frac{4}{7}

\frac{50 m}{4 + 3 m} = - 5

50 m = - 20 - 15 m

65 m = - 20

m = \frac{- 4}{13}

Commented by peter frank last updated on 28/Apr/19

t h a n k y o u