Find the equation to the common tangent of the circle x² + y² = 4ax and the parabola y²=4ax. The best explanatory answer will be marked as the brainliest.
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Answer:
The equation of any tangent to y
2
=4ax is
y=mx+
m
a
If it touches x
2
=4ay then, the equation.
x
2
=4a(mx+
m
a
) has equal roots.
mx
2
−4am
2
x−4a
2
=0 has equal roots
If the roots are equal, the discriminant is equal to 0
i.e.,b
2
−4ac=0
16a
2
m
4
+16a
2
m=0
16a
2
m
4
=−16a
2
m
m=−1
Putting m=−1 in y=mx+am we get,
y=−x−a
x+y+a=0 This is the common tangent to the two parabola.
Step-by-step explanation:
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