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

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 \dots

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