Question

t1’ and ‘t2’ are two points on the parabola y2 = 4x. If the chord joining them is a normal to the parabola at ‘t1’ then

Solution

Correct option is

t1(t1 + t2) + 2 = 0

The equation of chord is 

        

Now slope of normal at ‘t1’ is – t1. So chord will be normal att1if

            

SIMILAR QUESTIONS

Q1

The locus of the point of intersection of the lines bxt – ayt = ab and bx + ay = abt is 

Q2

The line  will touch the parabola y2 = 4a(x + a), if

Q3

The equation of the parabola whose axis is vertical and passes through the points (0, 0), (3, 0) and (–1, 4), is

Q4

The points on the parabola y2 = 36x whose ordinate is three times the abscissa are

Q5

The points on the parabola y2 = 12x whose focal distance is 4, are

Q6

Axis of the parabola x2 – 4x – 3+ 10 = 0 is  

Q7

The equation of the latus rectum of the parabola x2 + 4x + 2= 0 is 

Q8

x – 2 = t2y = 2t are the parameter equations of the parabola 

Q9

The equation  represents a parabola if  is

Q10

The vertex of the parabola y2 = 8x is at the center of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is