IPMAT Indore 2023 - QA (MCQ) Q35 Explanation

Explanation:

(a)

Equation of circle x^2 + y^2 − 6x + 4y − 12 = 0

Comparing above equation with general equation of circle x^2 + y^2 + 2gx + 2fy + c = 0

g = -3, f = 2, c = -12

Coordinate of center (- g, -f) ⇒ C(3,-2)

Radius = √g^2 + f^2 − c = √(−3)^2+ (2)^2 − (−12)

= √9 + 4 + 12 = √25 = 5

Now looking at the option, equation of lines in all the option represents the equation of parallel lines. (same slope)

Distance between 2 parallel lines (tangents) should be equal to the diameter of the circle = 2 x radius = 5 × 2 = 10

Distance between two parallel lines ax + by + c1=0 & ax + by + c2=0 = | c1 − c2 / √a^2+b^2 |

Checking option (a)

∴ Distance between the two parallel lines = |19 − (−31)/√4^2 + 3^2 |

= |50/5| = 10

Only equation of lines given in option (a) satisfies the condition and no other. Ans.