Find interms of a,b the value of c which makes the line y=mx+c a tangent to the parabola y^2 =4ax.also obtain the coordinate of the point of contact b) find the equation of tangent (x^2 /4)+(y^2 /9)=1 with gradient 2


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Question Number 50977 by peter frank last updated on 22/Dec/18

$F i n d i n t e r m s o f a, b t h e$ $v a l u e o f c w h i c h m a k e s$ $t h e l i n e y = m x + c$ $a t a n g e n t t o t h e p a r a b o l a$ $y^{2} = 4 a x . a l s o o b t a i n t h e$ $c o o r d i n a t e o f t h e p o i n t o f$ $c o n t a c t$ $b) f i n d t h e e q u a t i o n o f$ $t a n g e n t \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1 w i t h$ $g r a d i e n t 2$
	Answered by tanmay.chaudhury50@gmail.com last updated on 23/Dec/18

	${(m x + c)}^{2} = 4 a x$ $m^{2} x^{2} + 2 m c x + c^{2} = 4 a x$ $x^{2} (m^{2}) + x (2 m c - 4 a) + c^{2} = 0$ $r o o t s a r e e q u a l B^{2} = 4 A C$ ${(2 m c - 4 a)}^{2} = 4 m^{2} c^{2}$ $4 m^{2} c^{2} - 16 a m c + 16 a^{2} = 4 m^{2} c^{2}$ $- 16 a m c = - 16 a^{2}$ $c = \frac{a}{m}$
	Commented by peter frank last updated on 23/Dec/18

	$t h a n k y o u s i r .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 23/Dec/18

	$b) t a n n g e n t$ $y = m x + \sqrt{a^{2} m^{2} + b^{2}}$ $y = 2 x + \sqrt{16 + 9}$ $y = 2 x \pm 5$
	Commented by peter frank last updated on 23/Dec/18

	$t h a n k y o u$
	Commented by tanmay.chaudhury50@gmail.com last updated on 23/Dec/18

	$m o s t w e l c o m e . . .$
	Answered by peter frank last updated on 23/Dec/18

	$b) a^{2} = 4 b^{2} = 9 m = 2$ $y = m x + c$ $c^{2} = b^{2} + a^{2} m^{2}$ $c = \pm 5$ $y = 2 x \pm 5$
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