120968 If the focus of a parabola is \((0,-3)\) and its directrix is \(y=3\), then its equation is

120969 The points of intersection of the parabolas \(y^2=\) \(5 x\) and \(x^2=5 y\) lie on the line

120971 Let \(P\) represent the point \((3,6)\) on the parabola \(y^2=12 x\). For the parabola \(y^2=12 x\), if \(l_1\) is the length of the normal chord drawn at \(P\) and \(l_2\) is the length of the focal chord drawn through \(P\), then \(\frac{l_1}{l_2}=\)

120972 Study the following statements.
I. The vertex of the parabola \(x=l y^2+m y+n\) is
\(\left(\mathbf{n}-\frac{\mathbf{m}^2}{4 l},-\frac{\mathbf{m}}{2 l}\right)\)
II. The focus of the parabola \(y=1 x^2+\mathbf{m x}+\mathbf{n}\) is
\(\left(\mathrm{n}+\frac{1-\mathbf{m}^2}{4 l}, \frac{\mathrm{m}}{2 l}\right)\)
III. The pole of the line \(l \mathrm{x}+\mathrm{my}+\mathrm{n}=0\) with
respect to the parabola \(x^2=4 a y\) is
\(\left(-\frac{2 \mathbf{a} l}{\mathrm{~m}}, \frac{\mathbf{n}}{\mathbf{m}}\right)\)
The, the correct option among the following is

120968 If the focus of a parabola is \((0,-3)\) and its directrix is \(y=3\), then its equation is

120969 The points of intersection of the parabolas \(y^2=\) \(5 x\) and \(x^2=5 y\) lie on the line

120971 Let \(P\) represent the point \((3,6)\) on the parabola \(y^2=12 x\). For the parabola \(y^2=12 x\), if \(l_1\) is the length of the normal chord drawn at \(P\) and \(l_2\) is the length of the focal chord drawn through \(P\), then \(\frac{l_1}{l_2}=\)

120972 Study the following statements.
I. The vertex of the parabola \(x=l y^2+m y+n\) is
\(\left(\mathbf{n}-\frac{\mathbf{m}^2}{4 l},-\frac{\mathbf{m}}{2 l}\right)\)
II. The focus of the parabola \(y=1 x^2+\mathbf{m x}+\mathbf{n}\) is
\(\left(\mathrm{n}+\frac{1-\mathbf{m}^2}{4 l}, \frac{\mathrm{m}}{2 l}\right)\)
III. The pole of the line \(l \mathrm{x}+\mathrm{my}+\mathrm{n}=0\) with
respect to the parabola \(x^2=4 a y\) is
\(\left(-\frac{2 \mathbf{a} l}{\mathrm{~m}}, \frac{\mathbf{n}}{\mathbf{m}}\right)\)
The, the correct option among the following is

120968 If the focus of a parabola is \((0,-3)\) and its directrix is \(y=3\), then its equation is

120969 The points of intersection of the parabolas \(y^2=\) \(5 x\) and \(x^2=5 y\) lie on the line

120971 Let \(P\) represent the point \((3,6)\) on the parabola \(y^2=12 x\). For the parabola \(y^2=12 x\), if \(l_1\) is the length of the normal chord drawn at \(P\) and \(l_2\) is the length of the focal chord drawn through \(P\), then \(\frac{l_1}{l_2}=\)

120972 Study the following statements.
I. The vertex of the parabola \(x=l y^2+m y+n\) is
\(\left(\mathbf{n}-\frac{\mathbf{m}^2}{4 l},-\frac{\mathbf{m}}{2 l}\right)\)
II. The focus of the parabola \(y=1 x^2+\mathbf{m x}+\mathbf{n}\) is
\(\left(\mathrm{n}+\frac{1-\mathbf{m}^2}{4 l}, \frac{\mathrm{m}}{2 l}\right)\)
III. The pole of the line \(l \mathrm{x}+\mathrm{my}+\mathrm{n}=0\) with
respect to the parabola \(x^2=4 a y\) is
\(\left(-\frac{2 \mathbf{a} l}{\mathrm{~m}}, \frac{\mathbf{n}}{\mathbf{m}}\right)\)
The, the correct option among the following is

120968 If the focus of a parabola is \((0,-3)\) and its directrix is \(y=3\), then its equation is

120969 The points of intersection of the parabolas \(y^2=\) \(5 x\) and \(x^2=5 y\) lie on the line

120971 Let \(P\) represent the point \((3,6)\) on the parabola \(y^2=12 x\). For the parabola \(y^2=12 x\), if \(l_1\) is the length of the normal chord drawn at \(P\) and \(l_2\) is the length of the focal chord drawn through \(P\), then \(\frac{l_1}{l_2}=\)

120972 Study the following statements.
I. The vertex of the parabola \(x=l y^2+m y+n\) is
\(\left(\mathbf{n}-\frac{\mathbf{m}^2}{4 l},-\frac{\mathbf{m}}{2 l}\right)\)
II. The focus of the parabola \(y=1 x^2+\mathbf{m x}+\mathbf{n}\) is
\(\left(\mathrm{n}+\frac{1-\mathbf{m}^2}{4 l}, \frac{\mathrm{m}}{2 l}\right)\)
III. The pole of the line \(l \mathrm{x}+\mathrm{my}+\mathrm{n}=0\) with
respect to the parabola \(x^2=4 a y\) is
\(\left(-\frac{2 \mathbf{a} l}{\mathrm{~m}}, \frac{\mathbf{n}}{\mathbf{m}}\right)\)
The, the correct option among the following is