Let PQ be a focal chord of the parabola y2 = 4px. Let M be the...

Let PQ be a focal chord of the parabola y² = 4px. Let M be the midpoint of PQ. A perpendicular is drawn from M to the x-axis, meeting the x-axis at S. Also from M, a line segment is drawn that is perpendicular to PQ and that meets the x-axis at T. Show that the length of ST is one-half the focal width of the parabola.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

The base of a solid is the segment of the parabola y2 = 12x cut off...

The base of a solid is the segment of the parabola y2 = 12x cut off by the latus rectum. A section of the solid perpendicular to the axis of the parabola is a square. Find its volume.

Common tangent equation of y2 = 16x parabola and x2/36 - y2/20 = 1 hyperbola you...

Common tangent equation of y2 = 16x parabola and x2/36 - y2/20 = 1 hyperbola you find.

a) Find area between parabola f(x) = x^2/2p and its chord AB which is perpendicular to...

a) Find area between parabola f(x) = x^2/2p and its chord AB which is perpendicular to y-axis. Here A(a,f(a)), B(-a, f(-a)), a<0, p>0. b) Show also that this area is 2/3 of the area of the rectangle bounded by lines AB, X -axis, x = a,x = b.

Let AB be a diameter of a circle and suppose that UV is a perpendicular chord....

Let AB be a diameter of a circle and suppose that UV is a perpendicular chord. Show that cr(A,U,B,V)=2 (where cr = cross-ratio)

Find the vertex, focus, directrix, and focal width of the parabola. (y + 2)2 = -8(x...

Find the vertex, focus, directrix, and focal width of the parabola. (y + 2)2 = -8(x - 1)

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).

Let f(x, y) = − cos(x + y2 ) and let a be the point a...

Let f(x, y) = − cos(x + y2 ) and let a be the point a = ( π/2, 0). (a) Find the direction in which f increases most quickly at the point a. (b) Find the directional derivative Duf(a) of f at a in the direction u = (−5/13 , 12/13) . (c) Use Taylor’s formula to calculate a quadratic approximation to f at a.

(2) PQRS is a quadrilateral and M is the midpoint of PS. PQ = a, QR...

(2) PQRS is a quadrilateral and M is the midpoint of PS. PQ = a, QR = b and SQ = a – 2b. (a) Show that PS = 2b. Answer(a) [1] (b) Write down the mathematical name for the quadrilateral PQRM, giving reasons for your answer. Answer(b) .............................................................. because ............................................................... ............................................................................................................................................................. [2] __________ A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second. It continues at this speed for...

The Butterfly Theorem. Suppose M is the midpoint of a chord P Q of a circle...

The Butterfly Theorem. Suppose M is the midpoint of a chord P Q of a circle and AB and CD are two other chords that pass through M. Let AD and BC intersect P Q at X and Y , respectively. Then M is also the midpoint of XY . 1. Prove the Butterfly Theorem. [10] Hint: You know a lot about angles in a circle, and about triangles, and cross ratios, and all sorts of things . . .

In this question we show that we can use φ(n)/2. Let n = pq. Let x...

In this question we show that we can use φ(n)/2. Let n = pq. Let x be a number so that gcd(x, n) = 1. 1. show that xφ(n)/2 = 1 mod p and xφ(n)/2 = 1 mod q 2. Show that this implies that and xφ(n)/2 = 1 mod n 3. Show that if e · d = 1 mod φ(n)/2 then xe·d = 1 mod n. 4. How can we use φ(n)/2 in the RSA? Please explain answers...

Subjects