The Angle Between Lines Joining Origin To The Points Of Intersection Of The Line  and The Curve y2 – x2 = 4 Is

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Question

The angle between lines joining origin to the points of intersection of the line  and the curve y2 – x2 = 4 is

Solution

Correct option is

 

Lines joining origin to the point of intersection of the line  and the curve y2 – x2 = 4 are given by

        

,   compare with

ax2 + 2hxy + by2 = 0, we get a = 4, b = 0, h = 

Testing

SIMILAR QUESTIONS

Q1

Two straight lines pass through the fixed points  and have gradients whose product is k > 0. Show that the locus of the points of intersection of the lines is a hyperbola.

Q2

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6.

Q3

 

Find the range of ‘a’ for which two perpendicular tangents can be drawn to the hyperbola from any point outside the hyperbola

.

Q4

Find the hyperbola whose asymptotes are 2x – y = 3 and 3x + y – 7 = 0 and which passes through the point (1, 1).

Q5

The locus of a variable point whose distance from (–2, 0) is  times its distance from the line , is

Q6

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q7

Let P and , where , be two points on the hyperbola . If (h, k) is the point of intersection of the normal’s at P and Q, then k is equal to

Q8

If x = 9 is the chord of contact of the hyperbola x2 – y= 9, then equation of corresponding of tangents is

Q9

The locus of the mid-point of the chord of the circle x2 + y= 16, which are tangent to the hyperbola 9x2 – 16y= 144 is

Q10

If a circle cuts a rectangular hyperbola xy = c2 in A, B, C, D and the parameters of these four points be t1t2t3 and t4 respectively. Then