Let f be a focal point of hyperbola C, p be an intersection of a parallel line passing through F as an imaginary axis and hyperbola, and Q be an intersection of a parallel line passing through F as an asymptote and hyperbola, Then PF / QF =?

1/2.

Find the real axis length, focus coordinate, eccentricity, asymptote equation and vertex coordinate of hyperbola 16x2-9y2 = - 144

Hyperbola 16x2-9y2 = - 144 can be reduced to y216 − X29 = 1, so a = 4, B = 3, C = 5, so the real axis length is 8, the focus coordinates are (0,5) and (0, - 5), the eccentricity e = CA = 54, the asymptote equation is y = ± 43x, and the vertex coordinates are (0, ± 4)

The angle between two asymptotes of mathematical hyperbola is 60 degrees, what is the eccentricity
What is a progressive line

If the angle between an asymptote and the X axis is x, then the other asymptote is x + 60. If the sum of the slopes of the two asymptotes is 0, the sum of the slopes can be calculated by the sine theorem. In the curve, the slopes of the asymptotes are expressed by a and B. The two combinations can be divided into two cases. One is that the focus is on the X axis, or a and B can be taken out on the Y axis, so as to calculate the eccentricity below C

If the eccentricity of hyperbola is known as e, the tangent of the angle between its two asymptotes can be obtained

Let the focus of the hyperbola be on the x-axis, and the slopes of the two asymptotes be B / A, - B / A
Tangent of angle between two asymptotes = [B / a - (- B / a)] / [1 + B / a × (- B / a)] = (2B / a) / [1-B & sup2; / A & sup2;]
=2ab／（a²－b²）=2a√(c²－a²)／（2a²-c²）=2√（e²－1）／（2-e²）

Let f be a focal point of hyperbola C, p be an intersection of a parallel line passing through F as an imaginary axis and hyperbola, and Q be an intersection of a parallel line passing through F as an asymptote and hyperbola, Then PF / QF =?