JEE MAIN - Mathematics (2021 - 25th July Evening Shift - No. 19)
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 ______________.
Answer
1
Explanation
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 $$ \equiv y - 0 = {{4 - 0} \over {3 + 1}}(x + 1)$$
$$y = x + 1$$
y-intercept = 1
x2 + y2 + 2x = 0
Centre : ($$-$$1, 0)
Parabola : x2 $$-$$ 6x $$-$$ y + 13 = 0
(x $$-$$ 3)2 = y $$-$$ 4
Vertex : (3, 4)
Equation of line $$ \equiv y - 0 = {{4 - 0} \over {3 + 1}}(x + 1)$$
$$y = x + 1$$
y-intercept = 1
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