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# Analytical Math Problems

Analytical Geometry :
Analytical Geometry is a unit of mathematics with study of coordinate system,conic section,circle,equation of line.

Analytical Math Problem

1.  What is the center of the circle x+ y- 4x - y + 5 = 0

a) (2,1) b) (3,2) c)  (2,$\frac{1}{2}$) d)  (3,$\frac{1}{3}$)

2.  Express $\frac{21}{27}$ in standard form

a) $\frac{7}{-9}$            b) $\frac{3}{5}$ c) $\frac{7}{5}$ d) $\frac{-7}{4}$

3. IF xy, is an even integer then value of x and y is

a)  odd b)  even c)  an irrational number d)  none of the above

4. Calculate the gradient of the line AB  (1,-5)  and (4,6)

a)  $\frac{12}{3}$   b) $\frac{11}{3}$ c) $\frac{21}{7}$  d) $\frac{-11}{3}$

5. If Eccentricity is equal to 1,then the conic is called as

a)  Parabola b)  Ellipse     c) Hyperbola    d) None

6. Find the distance between A (3; 4) and B (6; 7)

a)  √9 b)  √3 c) 3√2     d)  0

7. Find the equation of the line with gradient = –2 passing through A (3,7)

a)  y = 2x + 3 b)  y = -2x + 1   c)  y = 2x + 5       d)  y = 5x + 3

8. the point (–6; –2) and perpendicular to 3x + 2y = 6

a)  $\frac{2}{3}$   b)  $\frac{3}{2}$    c)  $\frac{2}{5}$ d)  none

9. In the given figure, C is the midpoint of AB. Calculate the value of x and y.

10. Find the midpoint of the line joining A(-6; 4) and B(2;-5)

a)  (-2,-5)   b) (3,2) c)  (5,3) d)  (2,7)

11. What is the equation of Parabola

12. What is the standard form of equation of ellipse

Analytic Geometry Formula:

Mid point formula: $\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$

The distance formula is used to find the distance between two points A (x1 ; y1) and B (x2; y2)

AB = $\sqrt{\left ( X_{2}-X_{1} \right )^{2}+\left ( Y_{2}-Y_{1} \right )^{2}}$

The gradient of the line = $\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}$

The equation of a straight line is given by y = mx + c

The equation of the perpendicular bisector  = y – y1 = m(x – x1)