Angle of Intersection of Two Curves

Q. 38. If the normal to a parabola y²=4ax at P meets the curve again in Q and if PQ and the normal at Q makes angles alpha and beta respectively with the x-axis than {tan alpha(tan alpha +tan beta)} has the value equal to

Q. we know that slope of x axis is 0 and slope of y axis is infinity and x and y are perpendicular to each other than why the product of slope is not -1?

Q. Q.14 From the point A (0, 3) on the circle x^2+4x+(y-3)^{2 }= 0 a chord AB is drawn and extendedto a point M such that AM = 2 AB. The equation of the locus of M is:(A) x^2+8x+y^{2 } =0(C) (x-3)^2+8x y^2=0(B) x^2+8x+ (y-3)^2=0(D) x^2+8x+8y^2=0

Q. ntThe sides of a triangle touch y2=4ax and two of its angular points lie on y2=4b(x+c). Show that the locus of third angular point is another parabola.n

Q. { Find the equation of the circle passing through the intersection of the circles }x^2+y^2=4 and }}{x^2+y^2-2x-4y+4=0 and touching the line }x+2y=0 .

Q. The acute angle of intersection of the curves $y=[\left|\sin x\right|+\left|\cos x\right|]$ and $x^2+y^2=5$ (where $[.]$ denotes the greatest integer function) is ${\tan }^{-1}\left(k\right)$ then $k$ is

Q. Let $\theta$ be the acute angle between the curves $y=|x^2-2|$ and $y=\sqrt{8-x^2}$ at their point(s) of intersection. Then the value of $\tan \theta$ is

1. $0$
2. $\frac{3}{5}$
3. $\frac{5}{3}$
4. $1$

Q. The acute angle between the curves $y^2=x\mathrm{and}{x}^2=y$ at (1, 1) is .

1. ${\tan }^{-1}\frac{4}{3}$
2. ${\tan }^{-1}\frac{3}{4}$
3. $90°$
4. $45°$

Q. If the curves $x=y^4$ and $xy=k$ cut at right angles, then $(4k{)}^6$ is equal to

Q. Solve this:
Q. Find the equations of the chords of the parabola $y^2=4ax$ which pass through the point (- 6a, 0) and which subtends an angle of 45$°$ at the vertex.

Q.

The angle of intersection of the curves $y=2si{n}^{2}xandy=cos2xatx=\frac{\pi }{6}$ is

1. $\frac{\pi }{4}$

2. $\frac{\pi }{3}$

3. $\frac{\pi }{2}$

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