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Question

What's the equation of tangent to the parabola y2=4ax having a slope 'm'.


A

y=mx+am2

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B

y=mxam2

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C

y=mx+am

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D

y=mxam

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Solution

The correct option is C

y=mx+am


Given parabola is y2=4ax .........(1)

Let the tangent of the parabola be,

y=mx+c ..............(2)

for finding the tangent we solve the equations

of line and parabola and take the case when the number

of solution is equal to 1.

(mx+c)2=4ax

m2x2+2mcx+c2=4ax

m2x2+x(2mc4a)+c2=0

for having a single solution

=0

(2mc4a)24m2c2=0

4m2c2+16a216mca4m2c2=0

16a2=16mca

a=mc

c=am

Putting the value of c in (c) we get the equation of tangent as,

y=mx+am

From solving the line with the parabola we also get the point of contacts as (am2,2am)


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