Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsParabola

A focal chord of the parabola y^2 - 4x - 2y + 9 = 0 is tangent to the circle x^2 + y^2 - 12x - 2y + 34 = 0 . The length of this focal chord is equal to _____ .

Correct answer

12

Step-by-step solution

The given equation of the parabola is y^2 - 4x - 2y + 9 = 0 . Completing the square, we get: y^2 - 2y + 1 = 4x - 8 (y-1)^2 = 4(x-2) Comparing with (y-k)^2 = 4a(x-h) , we have 4a = 4 a = 1 . The focus of the parabola is (h+a, k) = (3, 1) . The given equation of the circle is x^2 + y^2 - 12x - 2y + 34 = 0 . Completing the square, we get: (x-6)^2 + (y-1)^2 = 36 + 1 - 34 = 3 The center of the circle is (6, 1) and its radius is 3 . Let the slope of the focal chord be m . Since it passes through the focus (3, 1) , its eq

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 2026Let 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 2026Let 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 2026Let 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 2026Let 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 2026Let 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 2026Consider 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 2026Let 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 JEE Main PYQs