Equation of Pair of Tangents: Hyperbola

Q. Find the equation of common tangent to the circle x^2+y^2-6x=0 and parabola y^2=4x is Solve by using slope form of both curves.

Q. 28. Let a variable line drawn from A(h, k) intersects the ellipse x+2y=1 at P and Q. The tangents at P and Q intersects at R and the locus of R is βx+(β+1)y=1. Find the values of β such that point A lies inside the ellipse

Q.

Find the angle between the tangents draws from the point (5, 3) to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$.

1. 

2. 

3. 

4. 

Q. 18. Find the equation(s) of the common tangent(s) of the curves y-6y-4x+9=0 and x+y-6x-6y+9=0

Q.

The distance between the parallel lines 4x-3y+5=0 and 4x-3y+15 =0 is:

1. 5 units

2. 2 units

3. 4 units

4. 3.5 units

Q.

The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x-y+1=0 is

1. 

2. 

3. 

4. 

Q. 101.Equation of tangent at P(1, 1) on a parabola with focus at (3, 4) be x+y=2 , Find equation of parabola and length of LR?

Q.

Find the equation of the tangents draws form the point (5, 3) to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1.$

1. 3x² - 5xy - 15x + 25y = 0

2. 3x² - 5xy + 10x + 15y = 0

3. 2x² - 5xy - 10x + 15y = 0

4. 2x² - 5xy - 15x + 25y = 0

Q. Two perpendicular tangents to the circle x^2+y^2=a^2 meet at P.Then the locus of P has the equation

Q. Deduce the equation of the tangent of a parabola y²=4ax ( y=mx+a/m)

Q. Let $P$ be the point of intersection of the common tangents to the parabola $y^2=12x$ and the hyperbola $8x^2-y^2=8.$ If $S$ and $S^{\prime }$ denote the foci of the hyperbola where $S$ lies on the positive $x-$axis then $P$ divides $S{S}^{\prime }$ in a ratio

1. $14:13$
2. $13:11$
3. $5:4$
4. $2:1$

Q. Tangents are drawn from any point on the circle $x^2+y^2=41$ to the Ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ then the angle between the two tangents is

1. $\frac{\pi }{4}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{6}$
4. $\frac{\pi }{2}$

Q.

Find the equation of the tangents drawn form the point (5, 3) to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1.$

1. $3x^2-5xy-15x+25y=0$

2. $3x^2-5xy+10x+15y=0$

3. $2x^2-5xy-10x+15y=0$

4. $2x^2-5xy-15x+25y=0$

Q. The equation of the pair of tangents drawn from the point (4, 3) to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ is .

1. $3x^2-4\mathrm{xy}-12x+16y=0$
2. $3x^2-2\mathrm{xy}-12x+16y=0$
3. $3x^2-8\mathrm{xy}-12x+16y=0$
4. $3x^2+4\mathrm{xy}-12x+16y=0$

Q. a curve c has a property that if a tangent at any point, say P, meets the axes at A and B then P is the midpoint of AB if the curve passes through (1, 1) find its equation.

Q. find the equation of common tangent y2-6y-4x+9=0 and x2+y2-6x-6y+9=0

Q. Find equation of circle tangent to 3x+y+3=0 at (-3, 6)& tangent to x+3y-7=0

Q. If the line y=mx+1 is tangent to the parabola y²=4x, then find the value of m.