Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2015MathematicsParabolaActual

If the tangent to the conic, y - 6 = x 2 at ( 2 , 10 ) touches the circle, x 2 + y 2 + 8 x - 2 y = k (for some fixed k ) at a point α , β ; then ( α , β ) is

Options

  1. A- 7 17 , 6 17
  2. B- 8 17 , 2 17
  3. C- 6 17 , 10 17
  4. D- 4 17 , 1 17

Correct answer

B. - 8 17 , 2 17

Step-by-step solution

The equation of tangent ( T = 0 ) would be 1 2   y + 10 -   6 = 2 x 4 x - y + 2 = 0 The center of the circle is ( - 4 , 1 ) and the point of contact would be the foot of perpendicular from ( - 4 , 1 ) on 4 x - y + 2 = 0 α + 4 4 = β - 1 - 1 =   - - 16 - 1 + 2 4 2 + 1 2 α + 4 4 = 15 17 and β - 1 - 1 = 15 17 α =   - 8 17 , β =   - 15 17 + 1 = 2 17 Hence option - 8 17 ,   2 17 is correct.

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