Question

A line passing through P (-2,3) meets the axes in A and B. If P divides AB in the ratio 3: 4. then the
equation of the line is
(A) 5x - 2y - 20 = 0 (B) 2x - y + 7 = 0 (C) x - 3y - 5 = 0 (D) 2x + y - 4 = 0

Step by step answer please. ​

Answer 1

Given :-

• A line passing through P (-2,3) meets the axes in A and B. If P divides AB in the ratio 3: 4.

To Find :-

The equation of the line is :-

(A) 5x - 2y - 20 = 0

(B) 2x - y + 7 = 0

(C) x - 3y - 5 = 0

(D) 2x + y - 4 = 0

Solution :-

we know that, point slop form of equation of a line is :-

• (y - y1) = m(x - x1)

Given that, line passes through P(-2, 3).

So,

→ y - 3 = m(x - (-2))

→ y - 3 = m(x + 2)

it is also said that, the line meets the axes in A and B. .

So ,

→ At x - intercept , y = 0

→ 0 - 3 = m(x + 2)

→ -3 = mx + 2m

→ mx = (-3) - (2m)

dividing both sides by m,

→ x = (-3/m) - 2

Therefore,

→ co - ordinate at x - intercept = {(-3/m) - 2} , 0

Similarly,

→ At y - intercept , x = 0.

→ y - 3 = m(0 + 2)

→ y - 3 = 2m

→ y = (2m + 3)

Therefore,

→ co - ordinate at y - intercept = (0, 2m + 3)

Now,

we know that :-

• section formula says that the coordinates of a point which divides the line joining two points (a,b) and (c,d) in the ratio m : n is given by = P ( x , y ) = (cm + an)/(m + n) , (dm + bn)/(m + n) .

we have now :-

• x = (-2)
• y = 3
• a = {(-3/m) - 2}
• b = 0
• c = 0
• d = 2m + 3
• m = 3
• n = 4

Putting all values we get :-

→ (-2) = [0*3 + {(-3/m) - 2}*4] / (3 + 4)

→ (-2) * 7 = 0 + 4{(-3/m) - 2}

→ (-14) = (-12/m) - 8

→ (-14) + 8 = (-12/m)

→ (-6) = (-12)/m

→ m = (-12)/(-6)

→ m = 2.

Hence,

Equation of line :-

→ y - 3 = m(x + 2)

→ y - 3 = 2(x + 2)

→ y - 3 = 2x + 4

→ y - 3 - 4 = 2x

→ y - 7 = 2x

→ 2x - y + 7 = 0 (Option B) (Ans.)

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