Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2007MathematicsParabola

The focus of the parabola y=2 x²+x is

Options

  1. A(0,0)
  2. B( 1 2 , 1 4 )
  3. C(- 1 4 , 0 )
  4. D(- 1 4 , 1 8 )

Correct answer

C. (- 1 4 , 0 )

Step-by-step solution

The given equation of parabola is y=2 x²+x ²+ x 2 = y 2 x²+ x 2 + 1 16 = y 2 + 1 16 (x+ 1 4 )²= 1 2 (y+ 1 8 ) where x+ 1 4 =X and y+ 1 8 =Y On comparing with X²=4 A Y , we get A= 1 8 focus of Eq. (i) is (0, 1 8 ) i.e. X=0, Y= 1 8 x+ 1 4 =0, y+ 1 8 = 1 8 x=- 1 4 , y=0 Focus of given parabola is (- 1 4 , 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 KCET PYQs