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A straight line is drawn through P(3,4) ...

A straight line is drawn through `P(3,4)` to meet the axis of `x` and `y` at `Aa n dB` , respectively. If the rectangle `O A C B` is completed, then find the locus of `Cdot`

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(x)+(4)/(y)=1`
Let the point C be (h,k).
Then the coordinates of A and B are `(h,0) and 90,k)`, respectively, Since points A,P, and B are collinear, we have
`|{:(h,,0,,),(3,,4,,),(0,,k,,),(h,,0,,):}|=0`
or `4h+3k-hk=0`
or `4x+3y-xy=0`
Therefore, the required locus is `(3)/(x)+(4)/(y)=1`
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