Intersection point of the tangents drawn to the parabola y2=4ax from the points (at12,2at1) and (at22,2at2) is

Question

Intersection point of the tangents drawn to the parabola y2=4ax from the points (at12,2at1) and (at22,2at2) is (A)  (at1t2,a(t1+t2))  (B)  (a(t1+t2),at1t2)  (C)  (t12t22,t1+t2)  (D) None of these

Tardigrade Admin · Accepted Answer

Equation of tangent to the parabola y2=4ax at the point (at12,2at1) is 2at1=2a(x+at12) ⇒ yt1=x+at12 ...(i) Similarly, equation of tangent at the point (at22,2at2) is 2yat2=2a(x+at22) ⇒ yt2=x+at22 ...(ii) On solving Eqs. (i) and (ii), we get y=a(t1+t2),x=at1t2 ∴ Intersection point [at1t2,a(t1+t2)]

Q. Intersection point of the tangents drawn to the parabola $y^{2} = 4 a x$ from the points $(a t_{1}^{2}, 2 a t_{1})$ and $(a t_{2}^{2}, 2 a t_{2})$ is

$(a t_{1} t_{2}, a (t_{1} + t_{2}))$

$(a (t_{1} + t_{2}), a t_{1} t_{2})$

$(t_{1}^{2} t_{2}^{2}, t_{1} + t_{2})$

None of these

Q. Intersection point of the tangents drawn to the parabola y2=4ax from the points (at12​,2at1​) and (at22​,2at2​) is

(at1​t2​,a(t1​+t2​))

(a(t1​+t2​),at1​t2​)

(t12​t22​,t1​+t2​)

None of these

Q. Intersection point of the tangents drawn to the parabola $y^{2} = 4 a x$ from the points $(a t_{1}^{2}, 2 a t_{1})$ and $(a t_{2}^{2}, 2 a t_{2})$ is

$(a t_{1} t_{2}, a (t_{1} + t_{2}))$

$(a (t_{1} + t_{2}), a t_{1} t_{2})$

$(t_{1}^{2} t_{2}^{2}, t_{1} + t_{2})$