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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 Q
ii)the midpoint of PQ

Grade:10

1 Answers

Ram Kushwah
110 Points
3 years ago
The equation of line is x+7y=5 and eqn of circle is : x²+y²=25
x+7y=5
so x=5-7y
Putting the value of x in the eqn of the circle
(5-7y)²+y²=25
25-70y+49y²+y²=25
50y²-70y=0
50y(y-70/50)=0
so y=0 or y= 7/5
Putting y= 0 in eqn of line
x+0=5, x=5
putting y=7/5
x+7*7/5=5
5x+49=25
5x=24
x=24/25
Thus The points P and Q are
P(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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