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Intersection of a Line and Finding Roots of a Parabola

If the line y...

Question

If the line y = x + 2a touches the parabola $y^{2} = 4 a (x + a)$ , then the point of contact is .

(0,a)

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(0,2a)

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(a,0)

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(2a,0)

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Solution

The correct option is B (0,2a)
Substituting y = x + 2a in the given equation of parabola, we get
${(x + 2 a)}^{2} = 4 ax + 4 a^{2} \Rightarrow x = 0$ .
Substituting x = 0 in y = x + 2a, we get y = 2a.
So, the point of contact is (0, 2a).

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