write the equation of the tangent line to the parabola at the point P.?

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TruBalla

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y=x^2
P=(a, a^2)

b) if the tangent line of part (a) must pass through the point Q=(1,-3), write an equation that the number "a" must satisfy.
 
Eq of tgt to parabola y = x^2

is ( y + y1 )/2 = x x1, where ( x1, y1 ) = ( a, a^2 ),

i.e., y + a^2 = 2 x ( a )

i.e., y = 2ax - a^2. ...................Ans.
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You would love this :

To write the eq of tgt to any conic ( circle, parabola,

ellipse, hyperbola )

Step - 1 : Replace x^2 by xx1, and y^2 by yy1.

Step - 2 : Replace x by ( x + x1 )/2, and y by ( y + y1 )/2.
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I am sure this will help you a lot in future.

Happy To Help !
 
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