Tangent and Normal to Circle
Conic Section

119873 The equation of polar of \((1,1)\) with respect to the circle \(x^2+y^2+4 x+6 y-3=0\) is

1 \(2 x+3 y-1=0\)
2 \(3 x+4 y+8=0\)
3 \(4 x+3 y+2=0\)
4 \(3 x+4 y+2=0\)
Conic Section

119874 The circle \(x^2+y^2+4 x-4 y+4=0\) touches

1 \(\mathrm{x}\) - axis only
2 \(y\)-axis only
3 \(x\)-axis and \(y\)-axis
4 \(x=y\)
Conic Section

119875 The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\). Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

1 \(2 \mathrm{x}-\sqrt{5} \mathrm{y}-20=0\)
2 \(2 x-\sqrt{5} y+4=0\)
3 \(3 \mathrm{x}-4 \mathrm{y}+8=0\)
4 \(4 x-3 y+4=0\)
Conic Section

119877 Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(\mathbf{x}+7=\mathbf{0}\) meets it.

1 \(7 x+y+50=0 \& 7 x-y+50=0\)
2 \(x+y=0 \& x-y=0\)
3 \(x+7 y+5=0 \& y-7 x+5=0\)
4 \(x+7 y+50=0 \& x-7 y+50=0\)
Conic Section

119878 The number of real tangents that can be drawn from \((1,1)\) to the circle \(x^2+y^2-6 x-4 y+4=0\), is

1 1
2 2
3 0
4 3
Conic Section

119873 The equation of polar of \((1,1)\) with respect to the circle \(x^2+y^2+4 x+6 y-3=0\) is

1 \(2 x+3 y-1=0\)
2 \(3 x+4 y+8=0\)
3 \(4 x+3 y+2=0\)
4 \(3 x+4 y+2=0\)
Conic Section

119874 The circle \(x^2+y^2+4 x-4 y+4=0\) touches

1 \(\mathrm{x}\) - axis only
2 \(y\)-axis only
3 \(x\)-axis and \(y\)-axis
4 \(x=y\)
Conic Section

119875 The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\). Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

1 \(2 \mathrm{x}-\sqrt{5} \mathrm{y}-20=0\)
2 \(2 x-\sqrt{5} y+4=0\)
3 \(3 \mathrm{x}-4 \mathrm{y}+8=0\)
4 \(4 x-3 y+4=0\)
Conic Section

119877 Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(\mathbf{x}+7=\mathbf{0}\) meets it.

1 \(7 x+y+50=0 \& 7 x-y+50=0\)
2 \(x+y=0 \& x-y=0\)
3 \(x+7 y+5=0 \& y-7 x+5=0\)
4 \(x+7 y+50=0 \& x-7 y+50=0\)
Conic Section

119878 The number of real tangents that can be drawn from \((1,1)\) to the circle \(x^2+y^2-6 x-4 y+4=0\), is

1 1
2 2
3 0
4 3
Conic Section

119873 The equation of polar of \((1,1)\) with respect to the circle \(x^2+y^2+4 x+6 y-3=0\) is

1 \(2 x+3 y-1=0\)
2 \(3 x+4 y+8=0\)
3 \(4 x+3 y+2=0\)
4 \(3 x+4 y+2=0\)
Conic Section

119874 The circle \(x^2+y^2+4 x-4 y+4=0\) touches

1 \(\mathrm{x}\) - axis only
2 \(y\)-axis only
3 \(x\)-axis and \(y\)-axis
4 \(x=y\)
Conic Section

119875 The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\). Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

1 \(2 \mathrm{x}-\sqrt{5} \mathrm{y}-20=0\)
2 \(2 x-\sqrt{5} y+4=0\)
3 \(3 \mathrm{x}-4 \mathrm{y}+8=0\)
4 \(4 x-3 y+4=0\)
Conic Section

119877 Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(\mathbf{x}+7=\mathbf{0}\) meets it.

1 \(7 x+y+50=0 \& 7 x-y+50=0\)
2 \(x+y=0 \& x-y=0\)
3 \(x+7 y+5=0 \& y-7 x+5=0\)
4 \(x+7 y+50=0 \& x-7 y+50=0\)
Conic Section

119878 The number of real tangents that can be drawn from \((1,1)\) to the circle \(x^2+y^2-6 x-4 y+4=0\), is

1 1
2 2
3 0
4 3
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Conic Section

119873 The equation of polar of \((1,1)\) with respect to the circle \(x^2+y^2+4 x+6 y-3=0\) is

1 \(2 x+3 y-1=0\)
2 \(3 x+4 y+8=0\)
3 \(4 x+3 y+2=0\)
4 \(3 x+4 y+2=0\)
Conic Section

119874 The circle \(x^2+y^2+4 x-4 y+4=0\) touches

1 \(\mathrm{x}\) - axis only
2 \(y\)-axis only
3 \(x\)-axis and \(y\)-axis
4 \(x=y\)
Conic Section

119875 The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\). Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

1 \(2 \mathrm{x}-\sqrt{5} \mathrm{y}-20=0\)
2 \(2 x-\sqrt{5} y+4=0\)
3 \(3 \mathrm{x}-4 \mathrm{y}+8=0\)
4 \(4 x-3 y+4=0\)
Conic Section

119877 Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(\mathbf{x}+7=\mathbf{0}\) meets it.

1 \(7 x+y+50=0 \& 7 x-y+50=0\)
2 \(x+y=0 \& x-y=0\)
3 \(x+7 y+5=0 \& y-7 x+5=0\)
4 \(x+7 y+50=0 \& x-7 y+50=0\)
Conic Section

119878 The number of real tangents that can be drawn from \((1,1)\) to the circle \(x^2+y^2-6 x-4 y+4=0\), is

1 1
2 2
3 0
4 3
Conic Section

119873 The equation of polar of \((1,1)\) with respect to the circle \(x^2+y^2+4 x+6 y-3=0\) is

1 \(2 x+3 y-1=0\)
2 \(3 x+4 y+8=0\)
3 \(4 x+3 y+2=0\)
4 \(3 x+4 y+2=0\)
Conic Section

119874 The circle \(x^2+y^2+4 x-4 y+4=0\) touches

1 \(\mathrm{x}\) - axis only
2 \(y\)-axis only
3 \(x\)-axis and \(y\)-axis
4 \(x=y\)
Conic Section

119875 The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\). Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

1 \(2 \mathrm{x}-\sqrt{5} \mathrm{y}-20=0\)
2 \(2 x-\sqrt{5} y+4=0\)
3 \(3 \mathrm{x}-4 \mathrm{y}+8=0\)
4 \(4 x-3 y+4=0\)
Conic Section

119877 Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(\mathbf{x}+7=\mathbf{0}\) meets it.

1 \(7 x+y+50=0 \& 7 x-y+50=0\)
2 \(x+y=0 \& x-y=0\)
3 \(x+7 y+5=0 \& y-7 x+5=0\)
4 \(x+7 y+50=0 \& x-7 y+50=0\)
Conic Section

119878 The number of real tangents that can be drawn from \((1,1)\) to the circle \(x^2+y^2-6 x-4 y+4=0\), is

1 1
2 2
3 0
4 3