Question

# If the tangents drawn from a point on the hyperbola to the ellipse make angles α and β with the transverse axis of the hyperbola, then

Hint:

### A hyperbola is the location of all the points on a plane whose distances from two fixed points in the plane differ by an amount that is always constant. We have given that the tangents drawn from a point on the hyperbola to the ellipse make angles α and β with the transverse axis of the hyperbola, we have to find the correct relation.

## The correct answer is:

### A hyperbola is a significant conic section in mathematics that is created by the intersection of a double cone with a plane surface, though not always at the centre. A hyperbola is symmetric along its conjugate axis and resembles the ellipse in many ways. A hyperbola is subject to concepts like foci, directrix, latus rectus, and eccentricity.

We have given: the tangents drawn from a point on the hyperbola to the ellipse make angles α and β with the transverse axis of the hyperbola.

So here we understood the concept of hyperbola and the normal lines.In analytic geometry, a hyperbola is a conic section created when a plane meets a double right circular cone at an angle that overlaps both cone halves. So the correct relation is

### Related Questions to study

### The eccentricity of the hyperbola whose latus rectum subtends a right angle at centre is

### The eccentricity of the hyperbola whose latus rectum subtends a right angle at centre is

### If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r^{2}t^{4}s^{2}, then the number of ordered pair (p, q) is –

Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple. Here we understood the concept of LCM and the pairs, so the total pairs can be 225.

### If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is r^{2}t^{4}s^{2}, then the number of ordered pair (p, q) is –

Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple. Here we understood the concept of LCM and the pairs, so the total pairs can be 225.

### A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length

Here we used the concept of number system and the rectangle, we can also solve it by permutation and combination. herefore, we get the number of rectangles possible with odd side length = m^{2}n^{2}.

### A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length

Here we used the concept of number system and the rectangle, we can also solve it by permutation and combination. herefore, we get the number of rectangles possible with odd side length = m^{2}n^{2}.

^{n}C_{r} + ^{2n}C_{r+1} + ^{n}C^{r+2} is equal to (2 r n)

^{n}C_{r} + ^{2n}C_{r+1} + ^{n}C^{r+2} is equal to (2 r n)

The coefficient of in is

The coefficient of in is