Find the equation of the straight line with a positive gradient which passes through the point (–5, 0) -Maths 9th

Find the equation of the straight line with a positive gradient which passes through the point (–5, 0) -Maths 9th
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(d) Both (a) and (c)Since the line passes through A(a, 0) and B(0, b), it makes intercepts a and b on x-axis and y-axis respectively. Let the equation of this line in the intercept from be \(rac{x}{a}\) + \(rac{y}{a}\) = 1By the given condition, AB = \(\sqrt{a^2+b^2}\) = 13 and ab = 60a2 + b2 = 169 ⇒ a2 + b2 + 2ab = 169 + 120 ⇒ (a + b)2 = 289 ⇒ a + b = ±17                 ...(i) Also, a2 + b2 – 2ab = 169 – 120 ⇒ (a – b)2 = 49 ⇒ a – b = ±7.                         ...(ii) ∴ From (i) and (ii) a = 12, b = 5 and a = –12, b = –5 ∴ The required equations of the straight line are:\(rac{x}{12}\) + \(rac{y}{5}\) = 1 and \(rac{x}{-12}\) + \(rac{y}{-5}\) = 1⇒ 5x + 12y = 60 and 5x + 12y + 60 = 0.
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