Position of a Point W.R.T Ellipse

Q. 15 Angle between the tangents drawn from point (4, 5) to the ellipse x/16 + y/25 = 1 is

Q. the equation of tangent to the parabola x^2=y at one extremity of latus rectum in the first quadrant is a)y=4x+1 b)x=4y+1 c)4x+4y=1 d)4x-4y=1

Q. Line joining the points (0, 3) and (5, -2) isa tangent to the curve y ax/1+x, then a∈\varnothing?

Q. An ellipse with major and minor axis length as $2a$ and $2b$ units touches coordinate axis in first quadrant. If foci are $(x_1,y_1)$ and $(x_2,y_2),$ then the value of $x_1{x}_2+y_1{y}_2$ is

1. $2a^2$
2. $2b^2$
3. $a^2{b}^2$
4. $a^2+b^2$

Q. the equation of tangent to the parabola y=2+4x-4x^2 with slope -4 is a)4x+y-6=0 b)4x+y+6=0 c)4x-y-6=0 d)none of these

Q. Is The equation of tangent yy1 = 2a(X+x1) at (x1, y1) is valid only for y square = 4ax or valid for all parabolas?

Q. { 43. From the point }(1, 1) tangents are drawn to the curve }}{ represented parametrically as }x=2t-t^2 and }y=t+t^2 . }} The distance between the points of contact is

Q. the equation of a tangent to the hyperbola 4x^2-5y^2=20 parallel to the line x-y=2 is a) x-y-3=0 b) x-y+1=0 c) x-y+9=0 d) x-y+7=0

Q. 22. Tangents are drawn from the point P(3, 4) to the ellipse x(sqr)/9 + y(sqr)/4 = 1 touching the ellipse at points A and B. Find the equation of the locus of the point whose distances from the point P and the line AB are equal.

Q. find the equation of tangent to the curve y is equals to under root x at the point where tangent drawn makes an angle pi by 4 with positive x axis

Q. 6. Angle between tangents drawn from point (4, 5) to ellipse x2/16 + y2/25=1 is

Q.

Find the set of values of $\alpha$ for which point the $P(\alpha ,-\alpha )$ is inside
$\frac{x^2}{16}+\frac{y^2}{9}=1$

1. $(\frac{-12}{5},\frac{12}{5})$
2. $[\frac{-12}{5},\frac{12}{5}]$
3. $(\frac{-13}{5},\frac{13}{5})$
4. $(\frac{-13}{5},\frac{13}{5}]$

Q. The line $3x+4y=\sqrt{7}$ touches the ellipse $3x^2+4y^2=1$ at the point

1. $(\sqrt{7},\sqrt{7})$
2. $(\frac{1}{\sqrt{7}},\frac{1}{\sqrt{7}})$
3. $(\frac{1}{\sqrt{7}},-\frac{1}{\sqrt{7}})$
4. $(-\sqrt{7},\sqrt{7})$

Q. An ellipse has eccentricity 1/2 and one focus at the point P(1/2, 1). Its one directrix is the common tangent, nearer to the point P, to the circle x2 + y2 = 1 and the hyperbola x2 - y2 = 1. The equation of the ellipse, in the standard form is .

Q. Consider a family of circles which are passing through M(1, 1) and are tangent to x-axis. If (h, k) be the center of the circle the
a) k > .5 c) 0 < k < .5
b) k < .5 d) -.5 < k < .5

Q. 84. A point on the line x+2y-5=from which twoperpendicular tangents can be drawn to the ellipse6x^2+4y^2 -24 = 0 is(1) , 3)(2) (1, 2)(223(4) (5, 0)

Q.

If for the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,S_1=\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}-1$, for point $(x_1,y_1)$, Which of the following is true

1. $S_1=0\Rightarrow (x_1,y_1)$ is on the ellipse
2. $S_1$$>0$$\Rightarrow (x_1,y_1)$ is inside the ellipse
3. $S_1$$<0$$\Rightarrow (x_1,y_1)$is outside the ellipse
4. $S_1$$>0$$\Rightarrow (x_1,y_1)$ is outside the ellipse