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In the Cartesian plane, two vertices of a square have coordinates (3 ; 4) and ( -2 ; - 1). One of the other two vertices, has coordibates
If the position vector of A and B are 3 −→a − 7 −→b − 7 −→c and 5 −→a + 4 −→b + 3−→c , nd −→AB and determine its magnitude and direction cosines.
Dilate the object by means of a scale factor of 1:5. Write down the coordinate points of the image. Expain whether any mention is made of symmetry between the object and the image. Describe abd explain the similarity between the object and the image.
The coordinates of the image of 𝑃(𝑥, 𝑦) when 𝑦 = 𝑓(𝑥) is transformed to
𝑦 = 2 𝑓(𝑥 − 3) − 1 are 𝑃′
(2, 3). Find the original point (𝑥, 𝑦).
<e> Find the equation of the sphere touching the plane 8𝑥 + 5𝑦 + 3𝑧 + 1 = 0 at (3, −1, −1) and cutting the sphere 𝑥2 + 𝑦2 + 𝑧2 − 2𝑥 + 𝑦 − 𝑧 − 6 = 0 orthogonally.
Graph two overlapping circles in the cartesian plane, such that the center of one another
lies at the circumference of the other.
• Show the standard and general equations of these circles inductively (meaning, writing
from its properties going to the equation).
• Graph also a parabola whose vertex is the center of one circle, and whose opening faces
the center of the other circle.
• Graph another parabola opposite to the first one whose endpoints of Latus Rectum are
the intersection points of the two circles.
• Show the standard and general equations of the parabolas inductively (meaning, writing
from its properties going to the equation).
How to find the coordinate of p and q if the circle cuts the x-axis at the points p and q in 2x^2 +2y^2 -8x +5y -10=0
Trace the conic 𝑥2 - 2xy + y2 -3x + 2y + 3 = 0
Find the equation of the line which is perpendicular to 4𝑦=5𝑥−8 and passing through (2,3).
𝐴(1,−2) is a point on the circle (𝑥−3)2+ (𝑦+1)2= 5
a. State the coordinates of the centre of the circle and hence find the coordinates of the point 𝐵 where 𝐴𝐵 is the diameter of the circle.
b. 𝐶(2,1) also lies on the circle. Use coordinate geometry to verify that angle 𝐴𝐶𝐵 = 900
