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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
	$AP is (y−0)=m(x−5) BQ is (y−0)=m(x+5) solve y=m(x−5) and 4x+3y=25 to find P 4x+3m(x−5)=25 4x+3mx−15m=25 x=((25+15m)/(4+3m)) and y=m(((25+15m)/(4+3m))−5) =m(((25+15m−20−15m)/(4+3m))) =(((5m)/(4+3m))) so P(((25+15m)/(4+3m)),((5m)/(4+3m))) now solve y=m(x+5) and 4x+3y=25 to find Q 4x+3m(x+5)=25 4x+3mx+15m=25 x=((25−15m)/(4+3m)),y=m(((25−15m)/(4+3m))+5) Q(((25−15m)/(4+3m)),(((25−15m+20+15m)/(4+3m)))×m (((25−15m�)/(4+3m)),((45m)/(4+3m))) PQ=(√({(_ ((25+15m)/(4+3m)))−_ (((25−15m_ )/(4+3m)))}^2 +(((45m−5m)/(4+3m)))^2 )) =(√(((900m^2 )/((4+3m)^2 ))+((1600m^2 )/((4+3m)^2 ))))=5 ((50m)/(4+3m))=5 50m−15m=20 m=((20)/(35))=(4/7) ((50m)/(4+3m))=−5 50m=−20−15m 65m=−20 m=((−4)/(13))$
	$A P i s (y - 0) = m (x - 5)$ $B Q i s (y - 0) = m (x + 5)$ $s o l v e y = m (x - 5) a n d 4 x + 3 y = 25 t o f i n d P$ $4 x + 3 m (x - 5) = 25$ $4 x + 3 m x - 15 m = 25$ $x = \frac{25 + 15 m}{4 + 3 m} a n d y = m (\frac{25 + 15 m}{4 + 3 m} - 5)$ $= m (\frac{25 + 15 m - 20 - 15 m}{4 + 3 m})$ $= (\frac{5 m}{4 + 3 m})$ $s o P (\frac{25 + 15 m}{4 + 3 m}, \frac{5 m}{4 + 3 m})$ $n o w s o l v e y = m (x + 5) a n d 4 x + 3 y = 25 t o f i n d Q$ $4 x + 3 m (x + 5) = 25$ $4 x + 3 m x + 15 m = 25$ $x = \frac{25 - 15 m}{4 + 3 m}, y = m (\frac{25 - 15 m}{4 + 3 m} + 5)$ $Q (\frac{25 - 15 m}{4 + 3 m}, (\frac{25 - 15 m + 20 + 15 m}{4 + 3 m}) \times m$ $(\frac{25 - 15 m}{4 + 3 m}, \frac{45 m}{4 + 3 m})$ $P Q = \sqrt{{(_{} \frac{25 + 15 m}{4 + 3 m}) -_{} (\frac{25 - 15 m_{}}{4 + 3 m})}^{2} + {(\frac{45 m - 5 m}{4 + 3 m})}^{2}}$ $= \sqrt{\frac{900 m^{2}}{{(4 + 3 m)}^{2}} + \frac{1600 m^{2}}{{(4 + 3 m)}^{2}}} = 5$ $\frac{50 m}{4 + 3 m} = 5$ $50 m - 15 m = 20$ $m = \frac{20}{35} = \frac{4}{7}$ $\frac{50 m}{4 + 3 m} = - 5$ $50 m = - 20 - 15 m$ $65 m = - 20$ $m = \frac{- 4}{13}$
	Commented by peter frank last updated on 28/Apr/19

	$t h a n k y o u$
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