NTA Abhyas JEE Main2020MathematicsParabolaPractice

The radius of circle, touching the parabola y 2 = 8 x a t 2,4 and passing through 0,4 , is

Options

A1 unit
B2 units
C2 units
D3 units

Correct answer

C. 2 units

Step-by-step solution

Equation of the tangent at 2,4 on the parabola y 2 = 8 x is y 4 = 8 x + 2 2 ⇒ y = x + 2 Let equation of circle touching line y = x + 2 at 2,4 is x - 2 2 + y - 4 2 + λ x - y + 2 = 0 which passes through 0,4 ⇒ 4 + 0 + λ 0 - 4 + 2 ⇒ λ = 2 ⇒ Equation of the required circle is x 2 + y 2 - 2 x - 10 y + 24 = 0 ⇒ The radius of the circle is 1 2 + 5 2 - 24 = 2

Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the tangent to the same parabola at another point (x₁, y₁) on the parabola. If L and T are perpendic 2026 Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the len 2026 Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of points P and Q are in the ratio 1:2 . If the chord PQ subtends an angle at the focus of the para 2026 Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing through the point P intersects the circle x^2 + y^2 - 2x - 4y + 3 = 0 at the points R and S , th 2026 Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , the 2026 Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16x . Let the vertex B containing the right angle be (4,8) and the locus of the cent 2026 Consider the parabola P : y^2 = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 = 1 . Let the line segment joining the points of intersection of P and E , be their latus rectums. If the 2026 Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p^2 + q^2 is: 2026 Full Parabola list All NTA Abhyas JEE Main PYQs