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The line x+7y=5 cuts the circle x x2+y yy2=25 at the points Pand Q.Find: i)Pand Q ii)the midpoint of PQ The line x+7y=5 cuts the circle xx2+yyy2=25 at the points Pand Q.Find:i)Pand Qii)the midpoint of PQ
The equation of line is x+7y=5 and eqn of circle is : x²+y²=25x+7y=5so x=5-7yPutting the value of x in the eqn of the circle(5-7y)²+y²=2525-70y+49y²+y²=2550y²-70y=050y(y-70/50)=0so y=0 or y= 7/5Putting y= 0 in eqn of linex+0=5, x=5putting y=7/5x+7*7/5=55x+49=255x=24x=24/25Thus The points P and Q areP(5,0) and Q(24/25,7/5)Now the coordinates of mid point of PQ is: { ( 5+24/25)/2, (0+7/5)/2)Or (149/50,7/10)
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