Question

A rod AB of length 15cm rests in between two co-ordinates axes in such a way that the end point A lies on X-axis and B lies on y-axis. A point P(x,y) is taken on the rod in such a way that Ap=6cm. Show that the locus of P is an ellipse. ?? Pls help me to solve this problem... Pls explain me it step by step......!!!!!!!!! Sun sir..??

Answer 1

The locus of P is an ellipse.

Given A lies on x axis = = > A = ( a , 0 )

Also B lies on y axis = = > B = ( 0 , b )

Given  P ( x , y ) such that AP = 6cm .

Also given length of rod  = AB = 15cm

From the figure, consider angle r.

In ΔBKP

• cos r =  adjacent side / hypotenuse = x / 9

In ΔALP

• sin r = opposite side / hypotenuse = y / 6

We know $cos^{2}r + sin^{2}r$ = 1

Therefore

• $(\frac{x}{9}) ^{2} + (\frac{y}{6}) ^{2}$ = 1
• Its clear that the equation is of an ellipse.
• Hence the locus of P is an ellipse