Question
Maths
Nov. 22, 2019, 11:01 p.m.
Answer
1) Show that 𝑥2 + 𝑥𝑦 − 6𝑦2 − 𝑥 − 8𝑦 − 2 = 0 represent a line pair and calculate their angle of intersection.
2) Show that the line pair through the origin respectively perpendicular to the line pair 𝑎𝑥2 + 2ℎ𝑥𝑦 + 𝑏𝑦2 = 0 is given by 𝑏𝑥2 − 2ℎ𝑥𝑦 + 𝑎𝑦2 = 0.
3) The straight line 𝑙𝑥 + 𝑚𝑦 + 𝑛 = 0 cuts the distinct pair of straight lines
𝑎𝑥2 + 2ℎ𝑥𝑦 + 𝑏𝑦2 = 0 at the points P and Q. If the angle OPQ equals the angle OQP,O being the origin. Show that ℎ(𝑙2− 𝑚2)= 𝑙𝑚(𝑎 − 𝑏).
4) Translate to the parallel axes through (4,-2) and hence simplify
16𝑥2 + 25𝑦2− 128𝑥 + 100𝑦 − 44 = 0.
5) Rotate axes for each of the following through the angle indicated.
I. 𝑥2 + 4𝑥𝑦 + 𝑦2 = 2 ; 450
II. 𝑥𝑦 + 𝑥 + 𝑦 = 0 ; 450
III. 4𝑥2 + 4𝑦2 = 17𝑥𝑦 ; 450
Maths
Nov. 22, 2019, 10:31 p.m.
Answer
The position vectors of the points A, B, C, D are 2𝒊 + 4𝒋 + 2𝒌, 𝒊 + 2𝒋 + 𝒌,
4𝒊 + 3𝒋 − 2𝒌, 3𝒊 + 𝒋 − 3𝒌. Show that AB is parallel to CD and that ABCD is a
parallelogram.
Maths
Nov. 22, 2019, 9:06 p.m.
Answer
By throwing a dice once, find the probability of getting a number greater than three
Maths
Nov. 22, 2019, 8:01 p.m.
Answer
, velocity of the boat in still water is 13 metre per second if the water flows in the river with a velocity of 5 metre per second what is the difference in time taken by him to cross the river in shortest path and in the shortest time if width of the river is 156mts