You visited us 1 times! Enjoying our articles? Unlock Full Access!

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)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(0,2a)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(a,0)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(2a,0)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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).

Suggest Corrections

Similar questions

y^{2} = 4 a (x + a)

x + y = 1

y^{2} - y + x = 0

P

y^{2} = 4 a x

x^{2} = 4 b y,

P

y = m x + c

y^{2} = 4 a (x + a)

y = m x + c

y^{2} = 4 a (x + a)

Join BYJU'S Learning Program