Consider the circle with centre at the origin and radius units

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Consider the circle with centre at the origin and radius

5

units. The points

P(3,4)

and

Q(4,3)

lie on this circle. Answer the following. (i) Verify that the points

P

and

Q

lie on the given circle. (ii) Find the coordinates of the midpoint

M

PQ

and hence determine the length

OM

. (iii) Calculate the length of chord

PQ

. (iv) Determine the slope of

PQ

and the slope of

OM

. What do you observe about the product of these slopes?