The equation of the tangent at (x1,y1) to a curve y2=4ax at a point (x1,y1) is given by yy1=2a(x+x1)
True
The situation can be repersented as below
We know that equation of tangent at (x1,y1) to a curve y=f(x) is given by
y−y1=[dydx](x1,y1)(x−x1)
curve is
y2=4ax
2y.dydx=4a
dydx=2ay
⇒[dydx](x1,y1)=2ay1
So the equation of tangent to y2=4ax at (x1,y1) is given by
y−y1=2ay1(x−x1)
yy1−y21=2ax−2ax1
substracting 2ax1 from both sides
yy1−y21−2ax1=2ax−4ax1
⇒yy1−2ax1=2ax(since y21=4ax1)
⇒yy1=2a(x+x1)
∴ The given statement is true