Question

The variable line drawn through the point (1.3) meets the x-axis at A and v-axis at B. If the rectangle
PB is completed. Where "O" is the origin, then locus of "P" is
​

Answer 1

YOUR ANSWER IS PRACTICALLY TOO IN ATTACHMENT ABOVE (SWIPE ATTACHMENT FROM RIGHT TO LEFT TO SEE ANSWER , there are total 4 pics of attachment)

P is the point whose locus we want to find and a line through(1,3) intersects the X axis at A and Y xis at B respectively. O is the origin.

so we get the equation on( h,k) and to get the locus convert h into x and k into y as done in the image ..Now it is in the form of general second degree conic equation … Now we shall identify the type of conic it represents..

we see that it by comparing our equation qith the general second degree equation and analysing the different condition of it we conclude the locus of the point P is hyperbola … infact rectangular hyperbola..!!

hope it helps

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