Question

the equation of a straight line passing through the point (-3,4) and that makes intercepts on the axis in the ratio 2:3 is ax+by+c=0 rhen a2+ b2+c2=?​

Answer 1

Answer:

I don't understand this question

Answer 2

Given data:

The equation of the straight line is passing through the point (3,-4) and making intercept which is in the ratio 2:3.

To find:

The equation of the straight line as detailed above.

Solution:

Given, the ratio of the intercepts a, b as a:b = 2:3

Then, x-intercept = 2m

          y-intercept = 3m

As we know that, the equation of the line is:  $\frac{x}{a}+\frac{y}{b}=1$

On substituting the x, y-intercepts, the line of equation will be

$\frac{x}{2m}+\frac{y}{3m}=1$

As this line is passing through the point (3, -4), substitute them in the above equation to get the value of m.

⇒ $\frac{3}{2m}+\frac{-4}{3m}=1$

⇒ $\frac{3}{2}+\frac{-4}{3}=m$

⇒ $\frac{9-8}{6}=m$

⇒ $m = \frac{1}{6}$

Substitute the value of:

x-intercept = 2($\frac{1}{6}$) = $\frac{1}{3}$

y-intercept = 3($\frac{1}{6}$) = $\frac{1}{2}$

Then, the equation will be:

⇒ $\frac{x}{\frac{1}{3} } + \frac{y}{\frac{1}{2} }=1$

⇒ 3x + 2y = 1

⇒ 3x + 2y - 1 = 0

Therefore, the equation of the straight line passing through the point (3,-4), making intercepts which are in the ratio 2:3 is

3x + 2y - 1 = 0

From the resultant equation, we get

a = 3

b = 2

c = -1

Then, a² + b² + c² = (3)² + (2)² + (-1)² = 9 + 4 + 1 = 14

Therefore, a² + b² + c² = 14

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