The-tangent-at-the-point-P-a-b-on-the-curve-y-ab-x-meets-the-x-axis-and-y-axis-at-Q-and-R-respectively-Show-that-PQ-RP-

Question Number 5615 by Rasheed Soomro last updated on 22/May/16

The tangent at the point P (a, b) on the

curve y = \frac{a b}{x} meets the x - axis and y - axis

at Q and R respectively . Show that

PQ = RP .

Commented by prakash jain last updated on 22/May/16

\frac{d y}{d x} = - \frac{a b}{x^{2}}

s l o p e o f t a n g e n t a t (a, b) = - \frac{a b}{a^{2}} = - \frac{b}{a}

e q u a t i o n o f t a n g e n t : y = m x + c

y = - \frac{b}{a} x + c

tangent passes thru (a, b)

b = - \frac{b}{a} a + c \Rightarrow c = 2 b

y = - \frac{b}{a} x + 2 b

x = 0 \Rightarrow y = 2 b o r R = (0, 2 b)

y = 0 \Rightarrow x = 2 a o r Q = (2 a, 0)

PQ = \sqrt{{(2 a - a)}^{2} + {(0 - b)}^{2}} = \sqrt{a^{2} + b^{2}}

QR = \sqrt{{(0 - a)}^{2} + {(2 b - b)}^{2}} = \sqrt{a^{2} + b^{2}}

PQ = QR

Commented by Rasheed Soomro last updated on 23/May/16

TH α n KS!

Always miss you when we {don}^{'} t see you

for some time in the activity of the forum!