Tangent and Normal of Parabola
Parabola

120230 A chord of the parabola \(y=x^2-2 x+5\) joins the point with the abscissas \(x_1=1, x_2=3\). Then the equation of the tangent to the parabola parallel to the chord is

1 \(2 x-y+2=0\)
2 \(2 x-y+1=0\)
3 \(2 x+y+1=0\)
4 \(2 x-y+\frac{5}{4}=0\)
Parabola

120231 The point of the contact of the tangent to the parabola \(y^2=4 a x\) which makes an angle of \(30^{\circ}\) with \(\mathrm{X}\)-axis, is

1 \((3 a, 2 \sqrt{3} a)\)
2 \((2 \sqrt{3} a, 3 a)\)
3 \((\sqrt{3} \mathrm{a}, 6 \mathrm{a})\)
4 None of these
Parabola

120232 A normal is drawn at a point \(\left(x_1, y_1\right)\) of the parabola \(y^2=16 x\) and this normal makes equal angle with both \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. Then, point ( \(\mathrm{x}_1\), \(\left.y_1\right)\) is

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

120233 The equation of the tangent to the curve \(y=4 e^{-x / 4}\) at the point where the curve crosses \(\mathbf{Y}\)-axis is equal to

1 \(3 x+4 y=16\)
2 \(4 x+y=4\)
3 \(x+y=4\)
4 \(3 x+4 y=25\)
Parabola

120234 The angle between tangents drawn from the origin to the parabola \(y^2=4 a(x-a)\) is

1 0
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{4}\)
4 \(\frac{\pi}{6}\)
Parabola

120230 A chord of the parabola \(y=x^2-2 x+5\) joins the point with the abscissas \(x_1=1, x_2=3\). Then the equation of the tangent to the parabola parallel to the chord is

1 \(2 x-y+2=0\)
2 \(2 x-y+1=0\)
3 \(2 x+y+1=0\)
4 \(2 x-y+\frac{5}{4}=0\)
Parabola

120231 The point of the contact of the tangent to the parabola \(y^2=4 a x\) which makes an angle of \(30^{\circ}\) with \(\mathrm{X}\)-axis, is

1 \((3 a, 2 \sqrt{3} a)\)
2 \((2 \sqrt{3} a, 3 a)\)
3 \((\sqrt{3} \mathrm{a}, 6 \mathrm{a})\)
4 None of these
Parabola

120232 A normal is drawn at a point \(\left(x_1, y_1\right)\) of the parabola \(y^2=16 x\) and this normal makes equal angle with both \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. Then, point ( \(\mathrm{x}_1\), \(\left.y_1\right)\) is

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

120233 The equation of the tangent to the curve \(y=4 e^{-x / 4}\) at the point where the curve crosses \(\mathbf{Y}\)-axis is equal to

1 \(3 x+4 y=16\)
2 \(4 x+y=4\)
3 \(x+y=4\)
4 \(3 x+4 y=25\)
Parabola

120234 The angle between tangents drawn from the origin to the parabola \(y^2=4 a(x-a)\) is

1 0
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{4}\)
4 \(\frac{\pi}{6}\)
Parabola

120230 A chord of the parabola \(y=x^2-2 x+5\) joins the point with the abscissas \(x_1=1, x_2=3\). Then the equation of the tangent to the parabola parallel to the chord is

1 \(2 x-y+2=0\)
2 \(2 x-y+1=0\)
3 \(2 x+y+1=0\)
4 \(2 x-y+\frac{5}{4}=0\)
Parabola

120231 The point of the contact of the tangent to the parabola \(y^2=4 a x\) which makes an angle of \(30^{\circ}\) with \(\mathrm{X}\)-axis, is

1 \((3 a, 2 \sqrt{3} a)\)
2 \((2 \sqrt{3} a, 3 a)\)
3 \((\sqrt{3} \mathrm{a}, 6 \mathrm{a})\)
4 None of these
Parabola

120232 A normal is drawn at a point \(\left(x_1, y_1\right)\) of the parabola \(y^2=16 x\) and this normal makes equal angle with both \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. Then, point ( \(\mathrm{x}_1\), \(\left.y_1\right)\) is

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

120233 The equation of the tangent to the curve \(y=4 e^{-x / 4}\) at the point where the curve crosses \(\mathbf{Y}\)-axis is equal to

1 \(3 x+4 y=16\)
2 \(4 x+y=4\)
3 \(x+y=4\)
4 \(3 x+4 y=25\)
Parabola

120234 The angle between tangents drawn from the origin to the parabola \(y^2=4 a(x-a)\) is

1 0
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{4}\)
4 \(\frac{\pi}{6}\)
Parabola

120230 A chord of the parabola \(y=x^2-2 x+5\) joins the point with the abscissas \(x_1=1, x_2=3\). Then the equation of the tangent to the parabola parallel to the chord is

1 \(2 x-y+2=0\)
2 \(2 x-y+1=0\)
3 \(2 x+y+1=0\)
4 \(2 x-y+\frac{5}{4}=0\)
Parabola

120231 The point of the contact of the tangent to the parabola \(y^2=4 a x\) which makes an angle of \(30^{\circ}\) with \(\mathrm{X}\)-axis, is

1 \((3 a, 2 \sqrt{3} a)\)
2 \((2 \sqrt{3} a, 3 a)\)
3 \((\sqrt{3} \mathrm{a}, 6 \mathrm{a})\)
4 None of these
Parabola

120232 A normal is drawn at a point \(\left(x_1, y_1\right)\) of the parabola \(y^2=16 x\) and this normal makes equal angle with both \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. Then, point ( \(\mathrm{x}_1\), \(\left.y_1\right)\) is

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

120233 The equation of the tangent to the curve \(y=4 e^{-x / 4}\) at the point where the curve crosses \(\mathbf{Y}\)-axis is equal to

1 \(3 x+4 y=16\)
2 \(4 x+y=4\)
3 \(x+y=4\)
4 \(3 x+4 y=25\)
Parabola

120234 The angle between tangents drawn from the origin to the parabola \(y^2=4 a(x-a)\) is

1 0
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{4}\)
4 \(\frac{\pi}{6}\)
Parabola

120230 A chord of the parabola \(y=x^2-2 x+5\) joins the point with the abscissas \(x_1=1, x_2=3\). Then the equation of the tangent to the parabola parallel to the chord is

1 \(2 x-y+2=0\)
2 \(2 x-y+1=0\)
3 \(2 x+y+1=0\)
4 \(2 x-y+\frac{5}{4}=0\)
Parabola

120231 The point of the contact of the tangent to the parabola \(y^2=4 a x\) which makes an angle of \(30^{\circ}\) with \(\mathrm{X}\)-axis, is

1 \((3 a, 2 \sqrt{3} a)\)
2 \((2 \sqrt{3} a, 3 a)\)
3 \((\sqrt{3} \mathrm{a}, 6 \mathrm{a})\)
4 None of these
Parabola

120232 A normal is drawn at a point \(\left(x_1, y_1\right)\) of the parabola \(y^2=16 x\) and this normal makes equal angle with both \(\mathrm{X}\) and \(\mathrm{Y}\)-axis. Then, point ( \(\mathrm{x}_1\), \(\left.y_1\right)\) is

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

120233 The equation of the tangent to the curve \(y=4 e^{-x / 4}\) at the point where the curve crosses \(\mathbf{Y}\)-axis is equal to

1 \(3 x+4 y=16\)
2 \(4 x+y=4\)
3 \(x+y=4\)
4 \(3 x+4 y=25\)
Parabola

120234 The angle between tangents drawn from the origin to the parabola \(y^2=4 a(x-a)\) is

1 0
2 \(\frac{\pi}{2}\)
3 \(\frac{\pi}{4}\)
4 \(\frac{\pi}{6}\)