Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20226 Jul 2022Morning ShiftMathematicsParabolaActual

The centre of the circle that passes through the point (0,1) and touches the curve y=x^2 at (2,4) is

Options

  1. A( -16 5 , 27 10 )
  2. B( -16 7 , 53 10 )
  3. C( -16 5 , 53 10 )
  4. D( -16 5 , -53 10 )

Correct answer

C. ( -16 5 , 53 10 )

Step-by-step solution

Let equation of circle is x^2+y^2+2 g x+2 f y+c=0 Where centre is (- g ,- f ) Since circle passes through (0,1) 0+1+0+2 f + c =0 c =2 f -1 (2,4) is also on the circle. aligned & 4+16+4 ~g +8 f -2 f -1=0 & 4 ~g +6 f -19=0 aligned Only option (c) satisfy 4 g+6 f-19=0

Practice Parabola on Quantrex Academy →

More from Parabola

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If P( , 4) is a point on this parabola such that the tangent to the parabola at point P passes thro 2026The distance of the focus of the parabola y^2 = 16x from its directrix is... 2026The area of the triangle formed by the lines joining the vertex of the parabola x^2 = 48y to the ends of its latus rectum, is ..... 2026A point on the parabola y^2 = 36 5 x at which the ordinate increases at thrice the rate of the abscissa is ..... 2026A circle is drawn with its centre at the focus of the parabola y^2=2 p x such that it touches the directrix of the parabola. Then a point of intersection of the circle and the para 2025If the locus of a point that divides a chord of slope 2 of the parabola y^2=4 x internally in the ratio 1: 2 is a parabola, then its vertex is 2025If x-y-3=0 is a normal drawn through the point (5,2) to the parabola y^2=4 x , then the slope of the other normal that can be drawn through the same point to the parabola y^2=4 x i 2025If the normal chord draw n at the point ( 15 2 , 15 2 ) to the parabola y ^2=15 x subtends an angle at the vertex of the parabola, then 3 + 2 3 - 4 3 = 2025 Full Parabola list All AP EAMCET PYQs