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The cartesian form is helpful to represent the geometric entities as algebraic expressions in three-dimensional geometry. Let us learn more about the conversion of cartesian form to vector form, the difference between cartesian form and vector form, with the help of examples, FAQs.
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The Cartesian plane is a number grid, like the one given on the right of this page. The numbers, or coordinates, on it allow us to locate the exact location of a point on the plane. There is a centre point, called the origin (O). Two axes are drawn through the origin to make the Cartesian plane.
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Question 2. A curve is defined by the following parametric equations. x = 4 at 2 , y = a ( 2 t + 1 ) , t ∈ . where a is non zero constant. Given the curves passes through the point A ( 4,0 ) , find the value of a . a = 4. 1, − t 2 = 2 x y = 3 ( t + 1 ) , t ∈ .
You are expected to know the following skills and concepts: graph parametric equations by hand by plotting points. graph a curve by eliminating the parameter from the equations, (i) by substitution to eliminate t or (ii) by using a Pythagorean identity, as appropriate.
6. Find the point on the y-axis that is equidistant to (2, 5) and (−1, 3). 7. Find the area of the triangle with vertices A(−2, −5), B(−2, 7), and C(10, 10). 8. Show that the triangle whose vertices are A(4, 15), B(12, 7), and C(−1, 2) is isosceles. 9. Sketch the graph of the circle defined by (x + 5)2 + y2 = 16.
