You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of Tangent at a Point (x,y) in Terms of f'(x)

If A 5, -2 ...

Question

If $A (5, - 2), B (2, 4)$ and point C lies on the locus $y = 1 = x + x^{2}$ , find the equation of the locus of centroid of $Δ A B C$

Open in App

Solution

$A (5, - 2), B (2, 4)$ and C lies on $y - 1 = x + x^{2}$
let C be $(x, y)$
=>centroid of $△ A B C = (\frac{5 + 2 + x}{3}, \frac{- 2 + 4 + y}{3}) = (h, k) => (x, y) = (3 h - 7, 3 k - 2)$
$(x, y)$ lies on $y - 1 = x + x^{2} => 3 k - 2 - 1 = 3 h - 7 + (3 h - 7)^{2} => 3 k - 3 = 3 h - 7 + 9 h^{2} - 42 h + 49 => 9 h^{2} - 39 h - 3 k + 45 = 0$
locus => $x^{2} - 13 x - y + 15 = 0$

Suggest Corrections

Similar questions

A (4, - 3), B (0, 2)

B

Y = 1 + x^{2}

△ A B C

A (5, 2), B (- 3, 5)

y = 2 + 3 x + x^{2}

△ A B C

A (6, - 1)

B (3, 5)

C

G

3 x^{2} - y^{2} = 1

Δ A B C,

B (1, 1), C (4, 2)

A

y = x + 3

(x - 1) (y - 2) = 5

(x - 1)^{2} + (y + 2)^{2} = r^{2}

A, B, C, D

Δ A B C

y = 3 x - 4

D

Join BYJU'S Learning Program