Question

When the axes rotated through an
angle900. The equation 5x - 2y + 7
O transforms to p.X + q + r = 0
Then 2p + q + r =
​

Answer 1

Transformation of Co-ordinates

Given: The axes are rotated through an angle 90°. Given equation 5x - 2y + 7 = 0 transforms to pX + qY + r = 0.

To find: the value of 2p + q + r = ?

Solution: Here the axes are rotated with the same origin.

The transformation formula be

x = X cos90° - Y sin90° = - Y

y = X sin90° + Y cos90° = X

Putting them in the given equation, we get

5 (- Y) - 2 (X) + 7 = 0

or, - 5Y - 2X + 7 = 0

or, 2X + 5Y - 7 = 0

Comparing it with pX + qY + r = 0, we get

p = 2, q = 5 and r = - 7 .

Now, 2p + q + r = 4 + 5 - 7 = 2

Answer: 2p + q + r = 2 .