Verified Solution • 2025–26 Session moderate

QJEEM21Maf051: JEE Main 2021 Mathematics - Class 11 JEEM21Maf051 Solution: The equation of a circle is Re(z 2 ) + 2(Im(z)) 2 + 2Re(z) = 0, …

The equation of a circle is Re(z2) + 2(Im(z))2 + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x2 −- 6x −- y + 13 = 0, has y-intercept equal to ______________.

Step-by-Step Verified Solution

Equation of circle is (x2 −- y2) + 2y2 + 2x = 0

x2 + y2 + 2x = 0

Centre : ( −- 1, 0)

Parabola : x2 −- 6x −- y + 13 = 0

(x −- 3)2 = y −- 4

Vertex : (3, 4)

Equation of line ≡y−0=4−03+1(x+1)\equiv y - 0 = {{4 - 0} \over {3 + 1}}(x + 1)

y=x+1y = x + 1

y-intercept = 1

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