1. ## [Coordinate Geometry] Locus

A point P moves along the arc of a circle with centre A(2,3). The arc passes through Q(-2,0) and R(5,k).
a) Find i)the equation of the locus of the point P
ii)the value of k

b) The tangent to the circle at point Q intersects(intercepts) the y-axis at point T. Find the area of triangle OQT .

P.S - I'm very weak in locus , anyone can tell me how can I improve it ?

2. ## coordinate geometry

Originally Posted by CallMeBin
A point P moves along the arc of a circle with centre A(2,3). The arc passes through Q(-2,0) and R(5,k).
a) Find i)the equation of the locus of the point P
ii)the value of k

b) The tangent to the circle at point Q intersects(intercepts) the y-axis at point T. Find the area of triangle OQT .

P.S - I'm very weak in locus , anyone can tell me how can I improve it ?
Hello Bin,

1 plot given points. QA is the radius of a circle because a circle is defined as the locus of points equidistant from a given point. Point P moves along the arc of a circle

2 Draw the slope diagram of QA. calculate the lenght of the hypotenuse which is the radius of the circle

3 Write the circle equation
(y-h)^2 +(x-k)^2 = r^2 where h=3 and k =2 and r= lenght of QA

4 Substitute 5 in this equation for x and solve for y the missing K not related to the k above

bjh

3. I don't understand the equation of the circle ..
Understood now .. Wonder why my teacher never teach o.o

and thanks !

4. ## coordinate geometry-circle

Originally Posted by CallMeBin
I don't understand the equation of the circle ..
Understood now .. Wonder why my teacher never teach o.o
Hello again Bin,

Go to website www.mathwarehouse.com and go to circles then standard equation of.

bjh

5. Originally Posted by bjhopper
Hello again Bin,

Go to website www.mathwarehouse.com and go to circles then standard equation of.

bjh
Hi bjh

The link is so useful .. let me try to do b)

Done, is it 25/3 ?

6. [quote=CallMeBin;506677]Hi bjh

The link is so useful .. let me try to do b)

Done, is it 25/3 ? [/quote

yes

bjh

,

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### coordinate geometry locus equation

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