If the points A(2,3) and B(3,2) form a triang | vedclass

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

Question

(B) Let the centroid of triangle $ABP$ be $G(x, y)$.The coordinates of the vertices are $A(2, 3)$,$B(3, 2)$,and $P(t, t^2)$.The centroid $G(x, y)$ is

Vedclass · Accepted Answer

$3x^2 - 10x - y + 10 = 0$

Vedclass · Answer

(B) Let the centroid of triangle $ABP$ be $G(x, y)$.The coordinates of the vertices are $A(2, 3)$,$B(3, 2)$,and $P(t, t^2)$.The centroid $G(x, y)$ is given by the formula:$x = \frac{2 + 3 + t}{3} \implies 3x = 5 + t \implies t = 3x - 5$$y = \frac{3 + 2 + t^2}{3} \implies 3y = 5 + t^2$Substitute $t = 3x - 5$ into the equation for $y$:$3y = 5 + (3x - 5)^2$$3y = 5 + 9x^2 - 30x + 25$$3y = 9x^2 - 30x + 30$Dividing by $3$:$y = 3x^2 - 10x + 10$Rearranging the terms:$3x^2 - 10x - y + 10 = 0$Thus,the locus of the centroid is $3x^2 - 10x - y + 10 = 0$.

If the points $A(2,3)$ and $B(3,2)$ form a triangle with a variable point $P(t, t^2)$,where $t$ is a parameter,then the equation of the locus of the centroid of triangle $ABP$ is:

Similar Questions

The locus of the mid-points of the chords of the circle $x^{2}+y^{2}+2x-2y-2=0$ which make an angle of $90^{\circ}$ at the centre is

$A$ company situated at $(2,0)$ in the $XY$-plane charges $RS. 2$ per $km$ for delivery. $A$ second company at $(0,3)$ charges $RS. 3$ per $km$ for delivery. The region of the plane where it is cheaper to use the first company is

$A$ circle passing through the origin cuts the coordinate axes at $A$ and $B$. If the straight line $AB$ passes through a fixed point $(x_1, y_1)$,then the locus of the centre of the circle is:

The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant,is a circle whose centre is at the

If a circle $S$ passing through the point $(3,4)$ cuts the circle $x^2+y^2=36$ orthogonally,then the locus of the centre of $S$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module