Question

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y2 = 8x, is 

Solution

Correct option is

Equation of chord of contact drawn from (x1y1) to parabola

                             y2 = 4ax is yy1 = 2a(x + x1)

 Equation of chord of contact drawn from (2, 5) to parabola

                             y2 = 8x                                         ... (1)

is                         5y = 4(x + 2)

                        4x – 5y + 8 = 0                              ... (2)

Point of intersection of (1) and (2) is y2 = 2(5y – 8)

                        y2 – 10y + 16 = 0

                         (y – 8)(y – 2) = 0 

                         y = 2, y = 8

                           y2 = 8x and y = 2  

 points are , (8, 8) and so length

                            .

SIMILAR QUESTIONS

Q1

The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse x2 + 2y2 = 6 which touch the ellipse x2 + 4y2 = 4 is

Q2

The normal at an end of a latus rectum of the ellipse  passes through an end of the minor axis if

Q3

If an ellipse slides between two perpendicular straight line, then the locus of its center is   

Q4

If the tangent at a point on the ellipse  meets the auxillary circle in two points, the chords joining them subtends a right angle at the center; then the eccentricity of the ellipse is given by

Q5

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin is

Q6

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Q7

Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents

Q8

The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.

Q9

The tangent at any point P of the hyperbola  makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then

Q10

The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is