he point of intersection of the circle x² + y² + 10x - 12y + 51 = 0 and the line 3y+x=3 is:
Explanation
Calculation:
Let the circle f(x, y) = x² + y² + 10x - 12y + 51 = 0 and the line g(x,y)=3y+x−3=0 intersect at a point P(a, b).
∴ g(a, b) = 0
3b + a - 3 = 0
⇒ a = 3 - 3b
... (1)
And, f(a, b) = 0
⇒ a² + b² + 10a - 12b + 51 = 0
⇒(3−3b)2+b2+10(3−3b)−12b+51=0
<br>⇒9−18b+9b2+b2+30−30b−12b+51=0
⇒10b2−60b+90=0
<br>⇒b2−6b+9=0
⇒(b−3)2=0
$$
Explanation
Calculation:
Let the circle f(x, y) = x² + y² + 10x - 12y + 51 = 0 and the line g(x,y)=3y+x−3=0 intersect at a point P(a, b).
∴ g(a, b) = 0
3b + a - 3 = 0
⇒ a = 3 - 3b
... (1)
And, f(a, b) = 0
⇒ a² + b² + 10a - 12b + 51 = 0
⇒(3−3b)2+b2+10(3−3b)−12b+51=0
<br>⇒9−18b+9b2+b2+30−30b−12b+51=0
⇒10b2−60b+90=0
<br>⇒b2−6b+9=0
⇒(b−3)2=0
$$
