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Solution :

Lert P(k,h) be a moving point and let `A(-5,1)` and `B(3,2)` be the given points. From the given condition,we have `angle APB=90^@` <br> Therefore, `DeltaAPB` is a right-angled triangle, Hence, <br> `AB^2=AP^2+PB^2` <br> or `(3+5)^2+(2-1)^2=(h+5)^2+(k-1)^2+(h-3)^2+(k-2)^2` <br> or `65=2(h^2+k^2+2h-3k)+39`<br> or `h^2+k^2+2h-3k-13=0` <br> Hence, the locus of `(h,k)` is `x^2+y^2+2x-3y-13=0`. **Theorem :-Every first degree equation in x,y represents a straight line.**

**Find the slope of a line when two points having coordinates are given ?**

**Find the slope of a line having equation of the form `ax+by+c=0`**

**Find the angles between two lines .**

**Examples :(i) Let A(6,4) and B(2,12) be two given points.Find the slope of the line perpendicular to AB. (ii) If line `3x-ay-1=0` is parallel to the line `(a-2)x-y+3=0` then find the values of a.**

**Condition for the parallelism of two lines.**

**Condition for Perpendicularity of two lines .**

**What is the intercept of a line on x- axis and y-axis ?**

**Equation of line parallel to x and y axis**

**Slope-intercept form of a line**