Tangent and Normal of Parabola
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Parabola

120996 What is the slope of the normal at the point \(\left(a t^2, 2 a t\right)\) of the parabola \(y^2=4 a x\) ?

1 \(\frac{1}{\mathrm{t}}\)
2 \(\mathrm{t}\)
3 \(-\mathrm{t}\)
4 \(-\frac{1}{\mathrm{t}}\)
BITSAT-2019
Parabola

120997 If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(x\)-axis, then

1 \(\alpha=2, \beta=-2\)
2 \(\alpha=-2, \beta=2\)
3 \(\alpha=2, \beta=2\)
4 \(\alpha=-2, \beta=2\)
Karnataka CET-2021
Parabola

120998 The point of contact of the tangent \(x+2 y+2=\) 0 with the parabola \(x^2=16 y\) is

1 \((2,-2)\)
2 \((4,1)\)
3 \((-4,1)\)
4 \((8,4)\)
COMEDK-2011
Parabola

120999 If \(y+b=m_1(x+a)\) and \(y+b=m_2(x+a)\) are two tangents to \(\mathrm{y}^2=4 \mathrm{ax}\), then

1 \(\mathrm{m}_1+\mathrm{m}_2=0\)
2 \(\mathrm{m}_1 \mathrm{~m}_2=1\)
3 \(\mathrm{m}_1 \mathrm{~m}_2=-1\)
4 None of these
COMEDK-2016
Parabola

121001 The condition that the line \(\frac{x}{p}+\frac{y}{q}=1\) be a normal to the parabola \(y^2=4 \mathrm{ax}\) is

1 \(\mathrm{p}^3=2 a \mathrm{p}^2+a \mathrm{q}^2\)
2 \(\mathrm{p}^3=2 \mathrm{aq}{ }^2+\mathrm{ap}^2\)
3 \(\mathrm{q}^3=2 \mathrm{ap}^2+\mathrm{aq} \mathrm{q}^2\)
4 None of these
VITEEE-2017
NEET DIGITAL LIBRARY
Parabola

120996 What is the slope of the normal at the point \(\left(a t^2, 2 a t\right)\) of the parabola \(y^2=4 a x\) ?

1 \(\frac{1}{\mathrm{t}}\)
2 \(\mathrm{t}\)
3 \(-\mathrm{t}\)
4 \(-\frac{1}{\mathrm{t}}\)
BITSAT-2019
Parabola

120997 If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(x\)-axis, then

1 \(\alpha=2, \beta=-2\)
2 \(\alpha=-2, \beta=2\)
3 \(\alpha=2, \beta=2\)
4 \(\alpha=-2, \beta=2\)
Karnataka CET-2021
Parabola

120998 The point of contact of the tangent \(x+2 y+2=\) 0 with the parabola \(x^2=16 y\) is

1 \((2,-2)\)
2 \((4,1)\)
3 \((-4,1)\)
4 \((8,4)\)
COMEDK-2011
Parabola

120999 If \(y+b=m_1(x+a)\) and \(y+b=m_2(x+a)\) are two tangents to \(\mathrm{y}^2=4 \mathrm{ax}\), then

1 \(\mathrm{m}_1+\mathrm{m}_2=0\)
2 \(\mathrm{m}_1 \mathrm{~m}_2=1\)
3 \(\mathrm{m}_1 \mathrm{~m}_2=-1\)
4 None of these
COMEDK-2016
Parabola

121001 The condition that the line \(\frac{x}{p}+\frac{y}{q}=1\) be a normal to the parabola \(y^2=4 \mathrm{ax}\) is

1 \(\mathrm{p}^3=2 a \mathrm{p}^2+a \mathrm{q}^2\)
2 \(\mathrm{p}^3=2 \mathrm{aq}{ }^2+\mathrm{ap}^2\)
3 \(\mathrm{q}^3=2 \mathrm{ap}^2+\mathrm{aq} \mathrm{q}^2\)
4 None of these
VITEEE-2017
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Parabola

120996 What is the slope of the normal at the point \(\left(a t^2, 2 a t\right)\) of the parabola \(y^2=4 a x\) ?

1 \(\frac{1}{\mathrm{t}}\)
2 \(\mathrm{t}\)
3 \(-\mathrm{t}\)
4 \(-\frac{1}{\mathrm{t}}\)
BITSAT-2019
Parabola

120997 If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(x\)-axis, then

1 \(\alpha=2, \beta=-2\)
2 \(\alpha=-2, \beta=2\)
3 \(\alpha=2, \beta=2\)
4 \(\alpha=-2, \beta=2\)
Karnataka CET-2021
Parabola

120998 The point of contact of the tangent \(x+2 y+2=\) 0 with the parabola \(x^2=16 y\) is

1 \((2,-2)\)
2 \((4,1)\)
3 \((-4,1)\)
4 \((8,4)\)
COMEDK-2011
Parabola

120999 If \(y+b=m_1(x+a)\) and \(y+b=m_2(x+a)\) are two tangents to \(\mathrm{y}^2=4 \mathrm{ax}\), then

1 \(\mathrm{m}_1+\mathrm{m}_2=0\)
2 \(\mathrm{m}_1 \mathrm{~m}_2=1\)
3 \(\mathrm{m}_1 \mathrm{~m}_2=-1\)
4 None of these
COMEDK-2016
Parabola

121001 The condition that the line \(\frac{x}{p}+\frac{y}{q}=1\) be a normal to the parabola \(y^2=4 \mathrm{ax}\) is

1 \(\mathrm{p}^3=2 a \mathrm{p}^2+a \mathrm{q}^2\)
2 \(\mathrm{p}^3=2 \mathrm{aq}{ }^2+\mathrm{ap}^2\)
3 \(\mathrm{q}^3=2 \mathrm{ap}^2+\mathrm{aq} \mathrm{q}^2\)
4 None of these
VITEEE-2017
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Parabola

120996 What is the slope of the normal at the point \(\left(a t^2, 2 a t\right)\) of the parabola \(y^2=4 a x\) ?

1 \(\frac{1}{\mathrm{t}}\)
2 \(\mathrm{t}\)
3 \(-\mathrm{t}\)
4 \(-\frac{1}{\mathrm{t}}\)
BITSAT-2019
Parabola

120997 If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(x\)-axis, then

1 \(\alpha=2, \beta=-2\)
2 \(\alpha=-2, \beta=2\)
3 \(\alpha=2, \beta=2\)
4 \(\alpha=-2, \beta=2\)
Karnataka CET-2021
Parabola

120998 The point of contact of the tangent \(x+2 y+2=\) 0 with the parabola \(x^2=16 y\) is

1 \((2,-2)\)
2 \((4,1)\)
3 \((-4,1)\)
4 \((8,4)\)
COMEDK-2011
Parabola

120999 If \(y+b=m_1(x+a)\) and \(y+b=m_2(x+a)\) are two tangents to \(\mathrm{y}^2=4 \mathrm{ax}\), then

1 \(\mathrm{m}_1+\mathrm{m}_2=0\)
2 \(\mathrm{m}_1 \mathrm{~m}_2=1\)
3 \(\mathrm{m}_1 \mathrm{~m}_2=-1\)
4 None of these
COMEDK-2016
Parabola

121001 The condition that the line \(\frac{x}{p}+\frac{y}{q}=1\) be a normal to the parabola \(y^2=4 \mathrm{ax}\) is

1 \(\mathrm{p}^3=2 a \mathrm{p}^2+a \mathrm{q}^2\)
2 \(\mathrm{p}^3=2 \mathrm{aq}{ }^2+\mathrm{ap}^2\)
3 \(\mathrm{q}^3=2 \mathrm{ap}^2+\mathrm{aq} \mathrm{q}^2\)
4 None of these
VITEEE-2017
NEET DIGITAL LIBRARY
Parabola

120996 What is the slope of the normal at the point \(\left(a t^2, 2 a t\right)\) of the parabola \(y^2=4 a x\) ?

1 \(\frac{1}{\mathrm{t}}\)
2 \(\mathrm{t}\)
3 \(-\mathrm{t}\)
4 \(-\frac{1}{\mathrm{t}}\)
BITSAT-2019
Parabola

120997 If the parabola \(y=\alpha x^2-6 x+\beta\) passes through the point \((0,2)\) and has its tangent at \(x=\frac{3}{2}\) parallel to \(x\)-axis, then

1 \(\alpha=2, \beta=-2\)
2 \(\alpha=-2, \beta=2\)
3 \(\alpha=2, \beta=2\)
4 \(\alpha=-2, \beta=2\)
Karnataka CET-2021
Parabola

120998 The point of contact of the tangent \(x+2 y+2=\) 0 with the parabola \(x^2=16 y\) is

1 \((2,-2)\)
2 \((4,1)\)
3 \((-4,1)\)
4 \((8,4)\)
COMEDK-2011
Parabola

120999 If \(y+b=m_1(x+a)\) and \(y+b=m_2(x+a)\) are two tangents to \(\mathrm{y}^2=4 \mathrm{ax}\), then

1 \(\mathrm{m}_1+\mathrm{m}_2=0\)
2 \(\mathrm{m}_1 \mathrm{~m}_2=1\)
3 \(\mathrm{m}_1 \mathrm{~m}_2=-1\)
4 None of these
COMEDK-2016
Parabola

121001 The condition that the line \(\frac{x}{p}+\frac{y}{q}=1\) be a normal to the parabola \(y^2=4 \mathrm{ax}\) is

1 \(\mathrm{p}^3=2 a \mathrm{p}^2+a \mathrm{q}^2\)
2 \(\mathrm{p}^3=2 \mathrm{aq}{ }^2+\mathrm{ap}^2\)
3 \(\mathrm{q}^3=2 \mathrm{ap}^2+\mathrm{aq} \mathrm{q}^2\)
4 None of these
VITEEE-2017