Tangent and Normal to Hyperbola
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Hyperbola

120776 The equation of the parabola with vertex at the origin and directrix \(y=2\) is

1 \(y^2=8 x\)
2 \(y^2=-8 x\)
3 \(y^2=\sqrt{8} x\)
4 \(x^2=-8 y\)
COMEDK-2018
Hyperbola

120777 The equation of tangents to the hyperbola \(3 x^2-2 y^2=6\), which is perpendicular to the line \(\mathbf{x}-\mathbf{3 y}=\mathbf{3}\), is

1 \(y=-3 x \pm \sqrt{15}\)
2 \(y=3 x \pm \sqrt{6}\)
3 \(y=-3 x \pm \sqrt{6}\)
4 \(y=2 x \pm \sqrt{15}\)
VITEEE-2015
Hyperbola

120778 The equation of the common tangents to the two
hyperbolas \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\), are

1 \(y= \pm x \pm \sqrt{b^2-a^2}\)
2 \(y= \pm x \pm \sqrt{a^2-b^2}\)
3 \(y= \pm x \pm \sqrt{a^2+b^2}\)
4 \(y= \pm x \pm \sqrt{a^2-b^2}\)
VITEEE-2010
Hyperbola

120779 If \(a x+b y=1\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then the value of \(a^2-b^2\) is

1 \(b^2 e^2\)
2 \(\frac{1}{b^2 e^2}\)
3 \(a^2 e^2\)
4 \(\frac{1}{\mathrm{a}^2 \mathrm{e}^2}\)
UPSEE-2018
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Hyperbola

120776 The equation of the parabola with vertex at the origin and directrix \(y=2\) is

1 \(y^2=8 x\)
2 \(y^2=-8 x\)
3 \(y^2=\sqrt{8} x\)
4 \(x^2=-8 y\)
COMEDK-2018
Hyperbola

120777 The equation of tangents to the hyperbola \(3 x^2-2 y^2=6\), which is perpendicular to the line \(\mathbf{x}-\mathbf{3 y}=\mathbf{3}\), is

1 \(y=-3 x \pm \sqrt{15}\)
2 \(y=3 x \pm \sqrt{6}\)
3 \(y=-3 x \pm \sqrt{6}\)
4 \(y=2 x \pm \sqrt{15}\)
VITEEE-2015
Hyperbola

120778 The equation of the common tangents to the two
hyperbolas \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\), are

1 \(y= \pm x \pm \sqrt{b^2-a^2}\)
2 \(y= \pm x \pm \sqrt{a^2-b^2}\)
3 \(y= \pm x \pm \sqrt{a^2+b^2}\)
4 \(y= \pm x \pm \sqrt{a^2-b^2}\)
VITEEE-2010
Hyperbola

120779 If \(a x+b y=1\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then the value of \(a^2-b^2\) is

1 \(b^2 e^2\)
2 \(\frac{1}{b^2 e^2}\)
3 \(a^2 e^2\)
4 \(\frac{1}{\mathrm{a}^2 \mathrm{e}^2}\)
UPSEE-2018
NEET DIGITAL LIBRARY
Hyperbola

120776 The equation of the parabola with vertex at the origin and directrix \(y=2\) is

1 \(y^2=8 x\)
2 \(y^2=-8 x\)
3 \(y^2=\sqrt{8} x\)
4 \(x^2=-8 y\)
COMEDK-2018
Hyperbola

120777 The equation of tangents to the hyperbola \(3 x^2-2 y^2=6\), which is perpendicular to the line \(\mathbf{x}-\mathbf{3 y}=\mathbf{3}\), is

1 \(y=-3 x \pm \sqrt{15}\)
2 \(y=3 x \pm \sqrt{6}\)
3 \(y=-3 x \pm \sqrt{6}\)
4 \(y=2 x \pm \sqrt{15}\)
VITEEE-2015
Hyperbola

120778 The equation of the common tangents to the two
hyperbolas \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\), are

1 \(y= \pm x \pm \sqrt{b^2-a^2}\)
2 \(y= \pm x \pm \sqrt{a^2-b^2}\)
3 \(y= \pm x \pm \sqrt{a^2+b^2}\)
4 \(y= \pm x \pm \sqrt{a^2-b^2}\)
VITEEE-2010
Hyperbola

120779 If \(a x+b y=1\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then the value of \(a^2-b^2\) is

1 \(b^2 e^2\)
2 \(\frac{1}{b^2 e^2}\)
3 \(a^2 e^2\)
4 \(\frac{1}{\mathrm{a}^2 \mathrm{e}^2}\)
UPSEE-2018
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Hyperbola

120776 The equation of the parabola with vertex at the origin and directrix \(y=2\) is

1 \(y^2=8 x\)
2 \(y^2=-8 x\)
3 \(y^2=\sqrt{8} x\)
4 \(x^2=-8 y\)
COMEDK-2018
Hyperbola

120777 The equation of tangents to the hyperbola \(3 x^2-2 y^2=6\), which is perpendicular to the line \(\mathbf{x}-\mathbf{3 y}=\mathbf{3}\), is

1 \(y=-3 x \pm \sqrt{15}\)
2 \(y=3 x \pm \sqrt{6}\)
3 \(y=-3 x \pm \sqrt{6}\)
4 \(y=2 x \pm \sqrt{15}\)
VITEEE-2015
Hyperbola

120778 The equation of the common tangents to the two
hyperbolas \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and \(\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\), are

1 \(y= \pm x \pm \sqrt{b^2-a^2}\)
2 \(y= \pm x \pm \sqrt{a^2-b^2}\)
3 \(y= \pm x \pm \sqrt{a^2+b^2}\)
4 \(y= \pm x \pm \sqrt{a^2-b^2}\)
VITEEE-2010
Hyperbola

120779 If \(a x+b y=1\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then the value of \(a^2-b^2\) is

1 \(b^2 e^2\)
2 \(\frac{1}{b^2 e^2}\)
3 \(a^2 e^2\)
4 \(\frac{1}{\mathrm{a}^2 \mathrm{e}^2}\)
UPSEE-2018
For More Updates join with Us