Find the centre of a circle passing through t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $O(x, y)$ be the centre of the circle. Let the points $A(6, -6), B(3, -7),$ and $C(3, 3)$ lie on the circumference.Since the distance from the

Vedclass · Accepted Answer

$(3, -2)$

Vedclass · Answer

(A) Let $O(x, y)$ be the centre of the circle. Let the points $A(6, -6), B(3, -7),$ and $C(3, 3)$ lie on the circumference.Since the distance from the centre to any point on the circle is equal (radius $r$):$OA^2 = OB^2 = OC^2$$OA^2 = (x - 6)^2 + (y + 6)^2$$OB^2 = (x - 3)^2 + (y + 7)^2$$OC^2 = (x - 3)^2 + (y - 3)^2$Equating $OB^2 = OC^2$:$(x - 3)^2 + (y + 7)^2 = (x - 3)^2 + (y - 3)^2$$(y + 7)^2 = (y - 3)^2$$y^2 + 14y + 49 = y^2 - 6y + 9$$20y = -40 \Rightarrow y = -2$Equating $OA^2 = OC^2$:$(x - 6)^2 + (y + 6)^2 = (x - 3)^2 + (y - 3)^2$Substitute $y = -2$:$(x - 6)^2 + (-2 + 6)^2 = (x - 3)^2 + (-2 - 3)^2$$(x - 6)^2 + 16 = (x - 3)^2 + 25$$x^2 - 12x + 36 + 16 = x^2 - 6x + 9 + 25$$-6x = -18 \Rightarrow x = 3$Thus,the centre is $(3, -2)$.

Find the centre of a circle passing through the points $(6, -6), (3, -7)$ and $(3, 3)$.

Similar Questions

In $\Delta ABC,$ if $A(0, 0), B(4, 0)$ and $C(0, 3)$ then $\Delta ABC$ is a $\ldots \ldots \ldots$ triangle.

If the vertices of $\Delta ABC$ are $A(9,5), B(6,7)$ and $C(3,3)$,then the length of median $\overline{BE}$ is.......

$A$ person begins his journey from point $A$. From $A$,he moves $800 \, m$ towards north to reach point $B$. From $B$,he moves $500 \, m$ towards east to reach point $C$. From $C$,he moves $400 \, m$ towards north to reach point $D$. Find the direct distance in $m$ from $A$ to $D$.

If the vertices of $\Delta PQR$ are $P(3, 10)$,$Q(6, 5)$,and $R(1, 2)$,then $\Delta PQR$ is a $\dots$ triangle.

If $A(-1, 4), B(2, 3)$ and $C(8, 1)$,then which of the following is true regarding the collinearity of points $A, B,$ and $C$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module