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Find the equation of the plane through the points (1,1,1),(-4,0,2) and (3,-1,0)
Find the sum of two vectors if one has a direction of 60 degree and a magnitude of 5 and the other has a direction of 240 and a magnitude of 2?
16x2+4y2+32x-16y-32=0
center,foci, ends of major and minor axis, ends of latus rectum
1.The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y 2 = 4ax. Prove that if P Q is a focal chord then the tangents to the curve at P and Q intersect at right angles at a point on the directrix.
2. The tangents at the points P(ap2 , 2ap) and Q(aq2 , 2aq) on the parabola y 2 = 4ax intersect at the point R. Given that the tangent at P is perpendicular to the chord OQ, where O is the origin, find the equation of the locus of R as p varies.
3. The coordinates of the ends of a focal chord of the parabola y 2 = 4ax are (x1, y1) and (x2, y2). Show that x1x2 = a 2 and y1y2 = −4a 2 .
4. Prove that the line x − 2y + 4a = 0 touches the parabola y 2 = 4ax, and find the coordinates of P, the point of contact. If the line x − 2y + 2a = 0 meets the parabola in Q, R, and M is the mid-point of QR, prove that PM is parallel to the axis of x, and that this axis and the line through M perpendicular to it meet on the normal at P to the parabola
If the position vector of one end of a chord through the focus of the parabola y^2 = 8x is 1/2i + 2j, find the position vector of the other end.
Find the midpoint and distance of the line segment that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) c) (-4.5, -12.5) and (4.5, 13)
1.) Find an equation for the plane that passes through the origin (0, 0, 0) and is parallel to the plane - x + 3y - 2z = 6
2.) Find the distance between the point (-1, - 2, 0) and the plane 3x - y + 4z =-2
1. Find the distance between the point and given plane.
P (1, 2, 3)
𝝅: 2x + y – 2z – 4 = 0
If the position vector of one end of a chord through the focus of the parabola y^2 = 8x is 1/2i + 2j, find the position vector of the other end.
A slender rod 40 in long is bent so as to form a right triangle. If the segments are 8 in and 32 in long, find the centroid.
