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there is a parabola with equation y 2 =8x and another ellipse (x 2 /4)+(y 2 /15)=1 find the equation of common tangent to both that parabola and ellipse

there is a parabola with equation y2=8x
and another ellipse (x2/4)+(y2/15)=1
find the equation of common tangent to both that parabola and ellipse
 

Grade:12th pass

1 Answers

Yasaschandra Dvs
25 Points
5 years ago
y^2 = 8x
=> y’ = 4/y
and  y’ for the ellipse would be 15(4-2x)/8y
gn that there exist acommon tanget => the slopes are same
=> 4/y = 15(4-2x)/8y
=> x = 14
sub x in the parabolla eqn 
=> y= sqrt(112)
wkt the formulae forfinding the equationof a tangent with gn slope is 
y-y1 = m(x-x1)
m 4/y =>4/sqrt(112)
sub in the eqn we get
ysqrt(112) -4x = 48 is the req eqn of the common tangent

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