Question
At which point the line x = my + 
touches the parabola x2 =4ay
- (2am, am2)
- (am2 , 2am)
Hint:
solve the 2 given equations to find the values of x and y.
The correct answer is:
(2a/m, a/m2)
Given, x= my+a/m => y = x/m – a/m2
Parabola : x2= 4ay
Substituting the value of y in the equation, we get
x2= 4a(x/m – a/m2 )
this gives us
m2x2 – 4amx -4a2 =0
on solving this quadratic equation, we get
x= 4am/2m2 = 2a/m
y = a/m2
point is (2a/m, a/m2)
the point of contact is the point of intersection between the 2 curves, the parabola and the line. this can be obtained by solving the two equations.
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