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Standard X

Mathematics

Collinearity Condition

The point x,y...

Question

The point (x,y) lies on the line joining (3,4) and (-5,-6) if

4x-5y=1

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5x-4y=1

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5x-4y+1=0

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4x+5y=1

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Solution

The correct option is B 5x-4y+1=0
Area of triangle = 0
or $= \frac{1}{2} [x (4 + 6) + 3 (- 6 - y) - 5 (y - 4)] = 0$
or v(10x - 8y + 2) = 0
or 5x - 4y + 1 = 0

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Similar questions

Q. Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

Find the equation of the circle orthogonal to the circles $x^{2} + y^{2} + 3 x - 5 y + 6 = 0 a n d 4 x^{2} + 4 y 2 - 28 x + 29 = 0$ and whose center lies on the line 3x + 4y + 1 = 0.

Q. Obtain the equation of the circle orthogonal to both the circles

x^{2} + y^{2} + 3 x - 5 y + 6 = 0

and

4 x^{2} + 4 y^{2} - 28 x + 29 = 0

and whose centre lies on the line

3 x + 4 y + 1 = 0

Q. If the point

(α, 0)

lies inside the quadrilateral formed by lines

2 x + 5 y = 15, 5 x - 4 y = 21, 3 x + 5 y + 17 = 0

and

y = x + 3

, then which of the following is

T R U E

Q. If

(α, 0)

lies inside the quadrilateral formed by lines

2 x + 5 y = 15

5 x - 4 y = 21

3 x + 5 y + 17 = 0

and

y = x + 3

.
Then

α

can be

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The point (x,y) lies on the line joining (3,4) and (-5,-6) if

The correct option is B 5x-4y+1=0Area of triangle = 0or =12[x(4+6)+3(−6−y)−5(y−4)]=0or v(10x - 8y + 2) = 0or 5x - 4y + 1 = 0

The correct option is B 5x-4y+1=0
Area of triangle = 0
or $= \frac{1}{2} [x (4 + 6) + 3 (- 6 - y) - 5 (y - 4)] = 0$
or v(10x - 8y + 2) = 0
or 5x - 4y + 1 = 0