Question
The foci of the ellipse,25 (x + 1)2 + 9 (y + 2)2 = 225, are at-
- (–1, 2) and (–1, –6)
- (–2, 1) and (– 2, 6)
- (– 1, – 2) and (–2, – 1)
- (–1, –2) and (–1, – 6)
Hint:
find out the values of a,b and e . find out the direction of major and minor axes so that the form of ellipse can be found out.
The correct answer is: (–1, 2) and (–1, –6)
(-1,2) and (-1,-6)
The given equation can be written as :
(x+1)2/9+(y+2)2/25=1
Here, a2=9=>a=3 and b2= 25=> b=5
Hence, we can see that b>a . so, the major axis is along y axis.
e2=1-a2/b2= 1-9/25=16/25 => e=4/5
foci : (x+1=0 , y+2= ±be)
be= 4/5 * 5 = 4
foci: (x=-1,y = ±4-2) = (-1,2) and (-1,-6)
the ellipse has its vertex at (-1,-2). The terms x+1 and y+2 can be replaced with X and Y for better understanding so that it gets converted into the standard form.
Related Questions to study
The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is-
this form of ellipse is a vertical one,i.e., the y axis is the major axis and the x axis is the minor axis.
The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is-
this form of ellipse is a vertical one,i.e., the y axis is the major axis and the x axis is the minor axis.
The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-
the focii are located at (ae,0) and (-ae,0). the distance between them is (ae-(-ae))= 2ae
similarly, the directrices are at a/e and -a/e .
The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-
the focii are located at (ae,0) and (-ae,0). the distance between them is (ae-(-ae))= 2ae
similarly, the directrices are at a/e and -a/e .
Ionization energies of five elements in kcal/mol are given below:
The element having most stable oxidation state +2 is ?
Ionization energies of five elements in kcal/mol are given below:
The element having most stable oxidation state +2 is ?
If line – 
+ 
= 
touches ellipse 
+ 
= 1 then its eccentric angle 
is
the general coordinates of an ellipse are substituted into the equation of ellipse to find the general equation of tangent of an ellipse. the angle lies in the 2nd quadrant so the cosine is negative but the sine is positive of the angle.
If line – + = touches ellipse + = 1 then its eccentric angle is
the general coordinates of an ellipse are substituted into the equation of ellipse to find the general equation of tangent of an ellipse. the angle lies in the 2nd quadrant so the cosine is negative but the sine is positive of the angle.
If latus rectum of ellipse x2tan2 + y2sec2 = 1 is 
then {0 < < 
/4} is equal to
the focal chord that is perpendicular to the major axis of the ellipse is called the latus rectum of the ellipse.
If latus rectum of ellipse x2tan2 + y2sec2 = 1 is then {0 < < /4} is equal to
the focal chord that is perpendicular to the major axis of the ellipse is called the latus rectum of the ellipse.
At infinite dilution, when the dissociation of electrolyte is complete, each ion makes a definite contribution towards the molar conductance of electrolyte, irrespective of the nature of the other ion with which it is associated.
The molar con conductance of an electrolyte at infinite dilute can be expressed as the sum of the contributions its individual ions.
Where x and y are the number of cations and anions respectively.
Answer the following questions:
Consider the following graph and state which of the following the correct statement is?
At infinite dilution, when the dissociation of electrolyte is complete, each ion makes a definite contribution towards the molar conductance of electrolyte, irrespective of the nature of the other ion with which it is associated.
The molar con conductance of an electrolyte at infinite dilute can be expressed as the sum of the contributions its individual ions.
Where x and y are the number of cations and anions respectively.
Answer the following questions:
Consider the following graph and state which of the following the correct statement is?
1 mol of [AgI]
can be coagulated by
1 mol of [AgI]can be coagulated by
A tangent to the ellipse 
+ 
= 1 is cut by the tangent at the extremities of the major axis at T and T' and the circle on TT' as diameter passes through the point Q, then Q may be -
A tangent to the ellipse + = 1 is cut by the tangent at the extremities of the major axis at T and T' and the circle on TT' as diameter passes through the point Q, then Q may be -
Tangent is drawn to ellipse 
at 
. Then the value of such that sum of intercepts on axes made by this tangent is minimum, is
Tangent is drawn to ellipse at . Then the value of such that sum of intercepts on axes made by this tangent is minimum, is
The eccentricity of the conic 9x2 + 4y2 –30y = 0 is
The eccentricity of the conic 9x2 + 4y2 –30y = 0 is
AgNO3(aq.) was added to an aqueous KCl Solution gradually and the conductivity of the Solution was measured. The plot of conductance versus the volume of AgNO3 is
AgNO3(aq.) was added to an aqueous KCl Solution gradually and the conductivity of the Solution was measured. The plot of conductance versus the volume of AgNO3 is
Assertion: The molecularity of a reaction is a whole number other than zero, but generally less than 
Reason : The order of a reaction is always whole number.
Assertion: The molecularity of a reaction is a whole number other than zero, but generally less than
Reason : The order of a reaction is always whole number.
The distance of the point '' on the ellipse 
from a focus is –
an ellipse has 2 focii at (ae,0 ) and (-ae,0) when the center is (0,0) and the ellipse has the x axis as its major axis. an ellipse is defined as the locus of a point whose sum of the distances from 2 fixed points (focii) is constant.
The distance of the point '' on the ellipse from a focus is –
an ellipse has 2 focii at (ae,0 ) and (-ae,0) when the center is (0,0) and the ellipse has the x axis as its major axis. an ellipse is defined as the locus of a point whose sum of the distances from 2 fixed points (focii) is constant.
At 
will be [Assume that the concentration of hydroquinone and quinine is (1M)]
At will be [Assume that the concentration of hydroquinone and quinine is (1M)]
Statement-I : If a, b, c are three positive numbers in G.P., then 
Statement-II : (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.
The relation between AM, GM and HM of a sequence states that (AM)(HM)=GM2
Statement-I : If a, b, c are three positive numbers in G.P., then
Statement-II : (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.
The relation between AM, GM and HM of a sequence states that (AM)(HM)=GM2
