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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)

Question:This was my girlfriend's extra credit problem last semester and no one in her class was able to solve it without using a calculator. Not even my girlfriend's aunt, who is a high school math teacher, was able to solve it. (7x - 2)^(1/3) + (7x + 5)^(1/3) = 3 I attempted both approaches in earnest and neither of them yielded anything I deemed useful. Thanks for the suggestions though.

Answers:Well, one answer is obviously 3/7, that can be found out just by looking upon the problem. Now, function x^(1/3) is monotone increasing (because f(x) is monotone increasing if f'(x)>0, and (x^(1/3))'=(1/3)x^(-2/3)>0), so (7x - 2)^(1/3), (7x + 5)^(1/3) and (7x - 2)^(1/3) + (7x + 5)^(1/3) are monotone increasing too, so the graphic of function f(x)=(7x - 2)^(1/3) + (7x + 5)^(1/3) can have only one point of crossing with any horizontal line, such as f(x)=3, and therefore it has only one salvation which is 3/7.

Question:What would be the absorbance of the gaseous ozone if its total pressure is doubled? This is a question from my professor. How to solve this problem? Thanks.=)

Answers:The Beer-Lambert Law states that absorbance is linearly proportional to the concentration of the ozone in your sample. So if the pressure is doubles, then so does the concentration. Absorbance doubles.

Question:I'm going back to school this fall and I plan on taking Calculus with Analytic Geometry I, II, III, instead of the other math classes like college algebra and calculus. I'm pursuing an engineering degree and that math class is required... (math is my worse subject.... 4 years ago) I dont remember much of the stuff at all really, but I'm thinking they teach you everything along the way anyway.. I dont remember everything from algebra or geometry either... But I plan on studying my butt off and working hard for a good grade so... Am I wasting my time for the inevitable F or no its a piece of cake and can be done no problem? Thanks all for your help and opinion~!