AP EAMCET202315 May 2023Evening ShiftMathematicsParabolaActual

The perpendicular distance from the origin to the focal chord drawn through the point (4,5) to the parabola y^2-4 y-3 x+7=0 is

Options

A2 5
B1 2
C1 5
D1

Correct answer

C. 1 5

Step-by-step solution

Given equation of parabola aligned & y^2-4 y-3 x+7=0 (y-2)^2=3(x-1) & (y-2)^2=4 3 4 (x-1) aligned So focus is ( 3 4 +1,2 )= ( 7 4 , 2 ) Now, equation of focal chord is y-5= 2-5 7 4 -4 (x-4) 4 x-3 y-1= Distance between focal chord & origin is |0-0-1| (-3)^2-4^2 = 1 5

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 2026 The distance of the focus of the parabola y^2 = 16x from its directrix is... 2026 The 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 ..... 2026 A point on the parabola y^2 = 36 5 x at which the ordinate increases at thrice the rate of the abscissa is ..... 2026 A 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 2025 If 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 2025 If 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 2025 If 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