Statement I: 4x^2+y^2-4xy-30x-50y+40=0 is the | vedclass

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(A) For Statement $I$: The definition of a parabola is the locus of a point $P(x,y)$ such that its distance from the focus $S(2,3)$ equals its distanc

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Statement $I$ is true,but statement $II$ is false

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(A) For Statement $I$: The definition of a parabola is the locus of a point $P(x,y)$ such that its distance from the focus $S(2,3)$ equals its distance from the directrix $x+2y+5=0$.$(x-2)^2 + (y-3)^2 = \frac{(x+2y+5)^2}{1^2+2^2}$$5(x^2-4x+4 + y^2-6y+9) = x^2+4y^2+25+4xy+10x+20y$$5x^2+5y^2-20x-30y+65 = x^2+4y^2+4xy+10x+20y+25$$4x^2+y^2-4xy-30x-50y+40=0$. Thus,Statement $I$ is true.For Statement $II$: Rewrite the equation $x^2-4x+16y+52=0$ as $(x-2)^2 = -16y-52+4 = -16(y+3)$.Comparing with $(x-h)^2 = -4a(y-k)$,we get $4a=16$,so $a=4$. The vertex is $(2,-3)$.The directrix is $y = k+a = -3+4 = 1$,or $y-1=0$. Statement $II$ is false.

Statement $I$: $4x^2+y^2-4xy-30x-50y+40=0$ is the equation of a parabola having $(2,3)$ as its focus and $x+2y+5=0$ as its directrix.
Statement $II$: The equation of the directrix of the parabola $x^2-4x+16y+52=0$ is $y+1=0$.
Which of the above statements is (are) true?

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Statement $I$: $4x^2+y^2-4xy-30x-50y+40=0$ is the equation of a parabola having $(2,3)$ as its focus and $x+2y+5=0$ as its directrix.Statement $II$: The equation of the directrix of the parabola $x^2-4x+16y+52=0$ is $y+1=0$.Which of the above statements is (are) true?