Statement 1 - The distance between the lines represented by $x^{2} + 22 x y + 2 y^{2} +$ $42 x + 4 y + 1 = 0$ is 2 .

Statement 2 - The distance between the lines $a x + b y + c = 0$ and $a x + b y + c_{1} = 0$ is $\frac{∣ c - c _{1} ∣}{a ^{2} + b ^{2}}$ .

Question

Statement 1 - The distance between the lines represented by $x^{2} + 22 x y + 2 y^{2} +$ $42 x + 4 y + 1 = 0$ is 2 .

Statement 2 - The distance between the lines $a x + b y + c = 0$ and $a x + b y + c_{1} = 0$ is $\frac{∣ c - c _{1} ∣}{a ^{2} + b ^{2}}$ .

TestHub · Accepted Answer

For the conic, a = 1 , b = 2 , h = 2 ​ , g = 2 2 ​ , f = 2 , c = 1. h 2 − ab = 0 and Δ = ab c + 2 f g h − a f 2 − b g 2 − c h 2 = 2 + 16 − 4 − 16 − 2 = − 4  = 0 . It is a parabola, not a pair of straight lines, so Statement 1 is false. Statement 2 is the standard formula and is true.

Mathematics - Straight Lines Question with Solution | TestHub

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