Question

If the straight line x + y = 1 touches the parabola y2 – y + x = 0, then the coordinates of the point of contact are

Solution

Correct option is

(0, 1)

        x + y = 1                                   … (1)

is tangent to parabola y2 – y + x = 0 its tangent is

      

 2yy­1 – y – y1 + x + x1 = 0

 x + y(2y1 – 1) = y1 – x1              … (2)

Compare (1) and (2),

    .

Point of contact is (0, 1).

 

SIMILAR QUESTIONS

Q1

If t is the parameter for one end of a focal chord of the parabola y2 = 4ax, then its length is

Q2

The point on the parabola y2 = 8x at which the normal is inclined at 600 to the x-axis has the coordinates

Q3

The length of the latus rectum of the parabola 9x2 – 6x + 36y + 19 = 0 is

Q4

The equation of a circle passing through the vertex the extremities of the latus rectum of the parabola y2 = 8x  is

Q5

If the parabola y2 = 4ax passes through the pint (1, –2), then the tangent at this point is

Q6

The equation of normal at the point  to the parabola y2 = 4ax, is

Q7

The equation of tangent at the point (1, 2) to the parabola y2 = 4ax, is

Q8

If a tangent of y2 = ax made angle of 450 with the x-axis, then its point of contact will be

Q9

If a normal drawn to the parabola y2 = 4ax at the point (a, 2a) meets parabola again on (at2, 2at), then the value of t will be

Q10

The angle of intersection between the curves y2 = 4x and x2 = 32y at point (16, 8) is