Home
Class 12
MATHS
The chord P Q of the rectangular hyperbo...

The chord `P Q` of the rectangular hyperbola `x y=a^2` meets the axis of `x` at `A ; C` is the midpoint of `P Q ;` and `O` is the origin. Then ` A C O` is equilateral (b) isosceles right-angled (d) right isosceles

Text Solution

AI Generated Solution

To solve the problem step-by-step, we will analyze the given information about the rectangular hyperbola and the points defined in the question. ### Step 1: Understand the Hyperbola The equation of the rectangular hyperbola is given by: \[ xy = a^2 \] ### Step 2: Identify Points - Let \( P \) and \( Q \) be points on the hyperbola. ...
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise EXERCISES|68 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWERS TYPE|18 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.5|5 Videos

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then DeltaACO is equilateral (b) isosceles right-angled (d) right isosceles

If cos^2A+cos^2B+cos^2C=1, t h e n ABC is (a)equilateral (b) isosceles (c)right angled (d) none of these

Tangents at P to rectangular hyperbola xy=2 meets coordinate axes at A and B, then area of triangle OAB (where O is origin) is _____.

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes at G and ga n dC is the center of the hyperbola, then (a) P G=P C (b) Pg=P C (c) P G=Pg (d) Gg=2P C

The triangle formed by complex numbers z ,i z ,i^2z is (a)Equilateral (b) Isosceles (c)Right angle (d) Scalene

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Q and R , then find the midpoint of chord Q Rdot

A tangent to the parabola x^2 =4ay meets the hyperbola xy = c^2 in two points P and Q. Then the midpoint of PQ lies on (A) a parabola (C) a hyperbola (B) an ellipse (D) a circle