Equation of Ellipse
- An ellipse can also be defined as the locus of a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant . Equation of an ellipse in standard form [x 2 /a 2 ]+[y 2 /b 2 ]=1 Let x'ox and yoy' be ..
General equation of a parabola
Let F(h,k) be the focus and the equation ax+by+c=0 be the equation of the directrix of a parabola. Let P(x,y) be any point on the parabola and let PM be the perpendicular drawn from p on the directrix . Then PF =PM => √(x-h) 2 +(y-k) 2 =ax+by+c/√a 2..
Theorem on Auxillary circle points at constant ratio
Proof : - Let P(x1,y1)be any point on an ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 And let Q(x1,y2) be its corresponding point on auxiliary circle (x 2 /a 2 )+(y 2 /a 2 ) = 1 Then (x1 2 /a 2 )+(y..
Equations of condition
Equations of condition - Study the following equations: a) 4x + 2 = 14 b) x - 7 = 5 - 2x c) 3a - 8 = a + 12 The equation 4x + 2 = 14 is true only when x = 3, Similarly, x - 7 = 5 - 2x is true only when x = 4, and 3a - 8 = a + 23 is true only when a = 10. The ..
Question 13
Question: Use a graph paper for this question. Draw the graphs of 2x-y-1 = 0 and 2x + y = 9 on the same axes. Use 2cm = 1unit on both the axes and plot only three points per line. Write down the co-ordinates of the point of intersection of the two lines...
Question: Use a graph paper for this question. Draw the graphs of 2x-y-1 = 0 and 2x + y = 9 on the same axes. Use 2cm = 1unit on both the axes and plot only three points per line. Write down the co-ordinates of the point of intersection of the two lines...General Equation of an Ellipse
- Let e be the eccentricity of an ellipse whose focus is F(p,q) and the equation of whose directrix is ax+by+c=0 Let P(x,y) be a point on the ellipse and PM be the perpendicular on directrix .Then by definition of ellipse PF/PM = e PF 2 = e 2 PM 2 (x-p) 2 + (..
intermediate algebra 2
Consider the ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 . Draw the lines ZD and ZD’ whose equations are x = a/e and x = -a/e respectively Let P(x,y) be any two points on the ellipse .Let D’PD be parallel to x-axis . The foci are F(c,o) a..
Consider the ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 . Draw the lines ZD and ZD’ whose equations are x = a/e and x = -a/e respectively Let P(x,y) be any two points on the ellipse .Let D’PD be parallel to x-axis . The foci are F(c,o) a..Summary
A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element...
Multiplication of Functions
As addition and subtraction, multiplication operation is also performed in functions. when f and g represents two functions. Multiplication of functions is given by f(x) * g(..
Identical equations or identities
The two expressions (LHS and RHS) are always equal for any value we give to the variable. Equations that are true for any value of the variable are called identical equations or briefly an identit..
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