Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2021MathematicsParabolaActual

Consider the region R= (x, y) R R : x 0 . and .y² 4-x . Let F be the family of all circles that are contained in R and have centers on the x -axis. Let C be the circle that has largest radius among the circles in F . Let ( , ) be a point where the circle C meets the curve y²=4-x . The value of α is _____.

Correct answer

0

Step-by-step solution

equation of normal at P is y - β = 2 β x - 4 + β 2 Passing through ( r , 0 ) ⇒ - 1 = 2 r - 4 + β 2   . . . i or    β = 0   . . . i i Also r 2 = r + β 2 - 4 2 + β 2   . . . i i i from i and i i i r = 3 2 , - 5 2 so radius of circle is 1 . 5 and α = 2 from i i and i i i r = 2 but in this case circle intersect at three points

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 Advanced PYQs