question_answer 31)

Find the area of the region {(x, y) :        

Answer:

Let R1 = {(x, y) : y2  4x}             R2 = {(x, y) : 4x2 + 4y2 9}        required region R =       For R1, consider y2 = 4x                   ? (1)                                   Put (1, 0) in y2 which is true        is the inside area of the parabola.       For R2, consider 4x2 + 4y2 = 9                      ... (2)             (2) represents a circle with centre (0, 0) and r       Put (1, 0) in 4x2 + 4y2              is the inside area of the circle.       Shaded area       Now (1) & (2)                   4x2 + 16x ? 9 = 0       4x2 + 16x ? 9 = 0       2x (2x + 9) ? 1 (2x + 9) = 0       (2x + 9) ? 1 (2x + 9) = 0       (2x + 9) (2x ? 1) = 0             [By (1)]                   Points of intersection are  and