Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202420 May 2024Morning ShiftMathematicsParabolaActual

A common tangent to the circle x^2+y^2=9 and parabola y^2=8 x is

Options

  1. A3 x- 3 y+2=0
  2. Bx- 3 y+6=0
  3. C2 x- 3 y+3=0
  4. Dx-3 y+6=0

Correct answer

B. x- 3 y+6=0

Step-by-step solution

Let y=m x+c be the equation of common tangent to parabola y^2=8 x and x^2+y^2=9 Condition for y=m x+c to be the tangent of y^2=4 a x is c= a m So, c= 2 m ....(i) The line y=m x+c is tangent to circle x^2+y^2=9 c m^2+1 =3 2 m^2+1 =3 m 4 m^2+1 =9 m^2 9 m^4+9 m^2-4=0 m^2= 1 3 , -4 3 m= 1 3 , -1 3 c=2 3 ,-2 3 y= 1 3 x+2 3 x- 3 y+6=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