Question

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

Solution

Correct option is

A hyperbola

bxt – ayt = ab                                … (1)  

       bx + ay = abt                          … (2)

(1)  bx – ay                           … (3)

For finding locus of intersectio0n of, we have to eliminate tfrom (2) and (3),

Multiplying (2) by (3), we get

        b2x2 – a2y2 = a2b2

   which is hyperbola.

SIMILAR QUESTIONS

Q1

Two tangent are drawn from the point (–2, –1) to the parabola y2 = 4x. if  is the angle between them, then 

Q2

The conic represented by the equation  is

Q3

If (4, 0) is the vertex and y-axis, the directrix of a parabola then its focus is

Q4

The straight line y = mx + c touches the parabola y2 = 4a(x + a) if

Q5

The focus of the parabola x2 – 2x – y + 2 = 0 is

Q6

If P1Q1 and P2Q2 are two focal chords of the parabola y2 = 4ax, then the chords P1P2 and Q1Q2 intersect on the

Q7

The condition that the line  be a normal to the parabola  

y2 = 4ax is

Q8

The equation of the normal to the hyperbola y2 = 4x, which passes through the point (3, 0), is

Q9

PQ is a double of the parabola y2 = 4ax. The locus of the points of trisection of PQ is

Q10

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