Tangent and Normal of Parabola
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Parabola

120266 The circle on focal radii of a parabola as diameter touches

1 the \(x\)-axis
2 the tangent at the vertex the
3 the directrix
4 None of the above
Parabola

120268 Tangent and normal are drawn at \(P(16,16)\) on the parabola \(y^2=16 x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle C P B=\theta\), then a value of \(\tan \theta\) is

1 \(\frac{1}{2}\)
2 2
3 3
4 \(\frac{4}{3}\)
Parabola

120269 Equation of a common tangent to the parabola \(y^2=4 x\) and the hyperbola \(x y=2\) is

1 \(x+2 y+4=0\)
2 \(x-2 y+4=0\)
3 \(4 \mathrm{x}+2 \mathrm{y}+1=0\)
4 \(x+y+1=0\)
Parabola

120270 The tangents to the curve \(y=(x-2)^2-1\) at its points of intersection with the line \(x-y=3\), intersect at the point

1 \(\left(\frac{5}{2}, 1\right)\)
2 \(\left(-\frac{5}{2},-1\right)\)
3 \(\left(\frac{5}{2},-1\right)\)
4 \(\left(-\frac{5}{2}, 1\right)\)
Parabola

120266 The circle on focal radii of a parabola as diameter touches

1 the \(x\)-axis
2 the tangent at the vertex the
3 the directrix
4 None of the above
Parabola

120268 Tangent and normal are drawn at \(P(16,16)\) on the parabola \(y^2=16 x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle C P B=\theta\), then a value of \(\tan \theta\) is

1 \(\frac{1}{2}\)
2 2
3 3
4 \(\frac{4}{3}\)
Parabola

120269 Equation of a common tangent to the parabola \(y^2=4 x\) and the hyperbola \(x y=2\) is

1 \(x+2 y+4=0\)
2 \(x-2 y+4=0\)
3 \(4 \mathrm{x}+2 \mathrm{y}+1=0\)
4 \(x+y+1=0\)
Parabola

120270 The tangents to the curve \(y=(x-2)^2-1\) at its points of intersection with the line \(x-y=3\), intersect at the point

1 \(\left(\frac{5}{2}, 1\right)\)
2 \(\left(-\frac{5}{2},-1\right)\)
3 \(\left(\frac{5}{2},-1\right)\)
4 \(\left(-\frac{5}{2}, 1\right)\)
Parabola

120266 The circle on focal radii of a parabola as diameter touches

1 the \(x\)-axis
2 the tangent at the vertex the
3 the directrix
4 None of the above
Parabola

120268 Tangent and normal are drawn at \(P(16,16)\) on the parabola \(y^2=16 x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle C P B=\theta\), then a value of \(\tan \theta\) is

1 \(\frac{1}{2}\)
2 2
3 3
4 \(\frac{4}{3}\)
Parabola

120269 Equation of a common tangent to the parabola \(y^2=4 x\) and the hyperbola \(x y=2\) is

1 \(x+2 y+4=0\)
2 \(x-2 y+4=0\)
3 \(4 \mathrm{x}+2 \mathrm{y}+1=0\)
4 \(x+y+1=0\)
Parabola

120270 The tangents to the curve \(y=(x-2)^2-1\) at its points of intersection with the line \(x-y=3\), intersect at the point

1 \(\left(\frac{5}{2}, 1\right)\)
2 \(\left(-\frac{5}{2},-1\right)\)
3 \(\left(\frac{5}{2},-1\right)\)
4 \(\left(-\frac{5}{2}, 1\right)\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Parabola

120266 The circle on focal radii of a parabola as diameter touches

1 the \(x\)-axis
2 the tangent at the vertex the
3 the directrix
4 None of the above
Parabola

120268 Tangent and normal are drawn at \(P(16,16)\) on the parabola \(y^2=16 x\), which intersect the axis of the parabola at \(A\) and \(B\), respectively. If \(C\) is the centre of the circle through the points \(P, A\) and \(B\) and \(\angle C P B=\theta\), then a value of \(\tan \theta\) is

1 \(\frac{1}{2}\)
2 2
3 3
4 \(\frac{4}{3}\)
Parabola

120269 Equation of a common tangent to the parabola \(y^2=4 x\) and the hyperbola \(x y=2\) is

1 \(x+2 y+4=0\)
2 \(x-2 y+4=0\)
3 \(4 \mathrm{x}+2 \mathrm{y}+1=0\)
4 \(x+y+1=0\)
Parabola

120270 The tangents to the curve \(y=(x-2)^2-1\) at its points of intersection with the line \(x-y=3\), intersect at the point

1 \(\left(\frac{5}{2}, 1\right)\)
2 \(\left(-\frac{5}{2},-1\right)\)
3 \(\left(\frac{5}{2},-1\right)\)
4 \(\left(-\frac{5}{2}, 1\right)\)